# Searching For Fermi GRB Optical Counterparts With The Prototype
Gravitational-Wave Optical Transient Observer (GOTO)

Y. -L. Mong,1,2 K. Ackley,1,2,3 D. K. Galloway1,2, M. Dyer4, R. Cutter3, M. J.
I. Brown1, J. Lyman3, K. Ulaczyk3, D. Steeghs3, V. Dhillon4, P. O’Brien5, G.
Ramsay6, K. Noysena7, R. Kotak8, R. Breton9, L. Nuttall10, E. Pallé11, D.
Pollacco3, E. Thrane1,2, S. Awiphan7, U. Burhanudin4, P. Chote3, A. Chrimes3,
E. Daw4, C. Duffy6, R. Eyles-Ferris5, B. Gompertz3, T. Heikkilä8, P. Irawati7,
M. Kennedy9, T. Killestein3, A. Levan3, S. Littlefair4, L. Makrygianni4, T.
Marsh3, D. Mata-Sanchez9, S. Mattila8, J. Maund4, J. McCormac3, D.
Mkrtichian7, J. Mullaney4, E. Rol1,2, U. Sawangwit7, E. Stanway3, R.
Starling5, P. Strøm3, S. Tooke5, K. Wiersema3

1School of Physics & Astronomy, Monash University, Clayton VIC 3800, Australia
2OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery,
Clayton VIC 3800, Australia
3Department of Physics, University of Warwick, Coventry, West Midlands, CV4
7AL, UK
4Department of Physics and Astronomy, University of Sheffield, Sheffield, S3
7RH, UK
5School of Physics and Astronomy, University of Leicester, University Road,
Leicester, LE1 7RH, UK
6Armagh Observatory & Planetarium, College Hill, Armagh, BT61 9DB, Co.Armagh,
Northern Ireland
7National Astronomical Research Institute of Thailand, 260 Moo 4, T. Donkaew,
A. Maerim, Chiangmai, 50180, Thailand
8Department of Physics and Astronomy, University of Turku, FI-20014 Turun
yliopisto, Finland
9Department of Physics and Astronomy, University of Manchester, M13 9PL, UK
10Institute of Cosmology and Gravitation, University of Portsmouth, Dennis
Sciama Building, Burnaby Road, Portsmouth, PO1 3FX, UK
11Instituto de Astrofísica de Canarias, E-38205 La Laguna, Tenerife, Spain
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The typical detection rate of $\sim 1$ gamma-ray burst (GRB) per day by the
_Fermi_ Gamma-ray Burst Monitor (GBM) provides a valuable opportunity to
further our understanding of GRB physics. However, the large uncertainty of
the _Fermi_ localization typically prevents rapid identification of multi-
wavelength counterparts. We report the follow-up of 93 _Fermi_ GRBs with the
Gravitational-wave Optical Transient Observer (GOTO) prototype on La Palma. We
selected 53 events (based on favourable observing conditions) for detailed
analysis, and to demonstrate our strategy of searching for optical
counterparts. We apply a filtering process consisting of both automated and
manual steps to 60 085 candidates initially, rejecting all but 29, arising
from 15 events. With $\approx 3$ GRB afterglows expected to be detectable with
GOTO from our sample, most of the candidates are unlikely to be related to the
GRBs. Since we did not have multiple observations for those candidates, we
cannot confidently confirm the association between the transients and the
GRBs. Our results show that GOTO can effectively search for GRB optical
counterparts thanks to its large field of view of $\approx 40$ square degrees
and its depth of $\approx 20$ mag. We also detail several methods to improve
our overall performance for future follow-up programs of _Fermi_ GRBs.

###### keywords:

transients: gamma-ray bursts – methods: observational

††pubyear: 2021††pagerange: Searching For Fermi GRB Optical Counterparts With
The Prototype Gravitational-Wave Optical Transient Observer (GOTO)–Searching
For Fermi GRB Optical Counterparts With The Prototype Gravitational-Wave
Optical Transient Observer (GOTO)

##  1 Introduction

It is generally believed that $\gamma$-ray bursts (GRBs) come from core-
collapse supernovae (SNe; MacFadyen & Woosley, 1999; MacFadyen et al., 2001;
Woosley & Bloom, 2006; Woosley, 2011) or compact binary coalescence (CBC;
Eichler et al., 1989; Paczynski, 1991; Kochanek & Piran, 1993; Bartos et al.,
2013; Rosswog et al., 2013). They are divided into two classes called long and
short GRBs based on the duration of the $\gamma$-ray burst with the boundary
historically set at $\sim 2\,{\rm s}$ (Kouveliotou et al., 1993; Sakamoto et
al., 2008, 2011; Zhang et al., 2012; Qin et al., 2013). Although GRBs have
been studied for more than 50 years since the first discovery on 2 July 1967
(Klebesadel et al., 1973), it was the simultaneous detection of GW170817 and
GRB170817A (LIGO Scientific Collaboration & Virgo Collaboration, 2017; Abbott
et al., 2017b, a; Goldstein et al., 2017; Savchenko et al., 2017) that the
progenitor origin of short GRBs as CBC sources was confirmed.

The Burst and Transient Source Experiment (BATSE; Goldstein et al., 2013)
launched in 1991, established the first step in GRB research by showing the
cosmological origin of GRBs. In order to explain the isotropic equivalent
luminosity of GRBs, which could be up to $\sim 10^{54}\,{\rm ergs}$ (Frail et
al., 2001), the fireball model was introduced (Paczynski, 1986; Goodman, 1986;
Shemi & Piran, 1990; Rees & Meszaros, 1992; Piran et al., 1993; Wijers et al.,
1997; Vietri, 1997; Mészáros et al., 2002). This model suggests that due to
relativistic outflows, the $\gamma$-ray emission is highly beamed with the
beaming angle of $\theta_{b}\sim 1/\Gamma$, where $\Gamma$ is the bulk Lorentz
factor of the outflow (Rhoads, 1999; Sari et al., 1999). The effect of
relativistic beaming can significantly reduce the energy such that it can
explain the energy scale of the GRB. The fireball model also invokes internal
and external shocks to explain the prompt $\gamma$-ray emission and the
afterglow (Blandford & McKee, 1976; Rees & Meszaros, 1994; Beloborodov, 2000).

In 1997, BeppoSAX (Boella et al., 1997) first enabled multi-wavelength
observations of GRB afterglows (Costa et al., 1997; van Paradijs et al., 1997;
Frail et al., 1997). The Wide Field Cameras (WFCs) on board BeppoSAX can track
GRB Monitor (GRBM) triggers to locate the GRBs with a precision of $\approx 3$
arcmin (Jager et al., 1997). The detection of X-ray counterparts can help
identify the optical counterpart, which can then be used to identify the host
galaxy and constrain the luminosity of the GRBs with its redshift (Metzger et
al., 1997). BeppoSAX also helped GRB980425 to be identified with SN1998bw
(Galama et al., 1998), which suggested that the origin of long GRBs is core-
collapse SNe (MacFadyen & Woosley, 1999; MacFadyen et al., 2001).

Today the discovery of GRBs is mainly made through the _Swift_ and _Fermi_
satellites. There are two narrow-field instruments on board _Swift_ — the
X-Ray Telescope (XRT; Burrows et al., 2005) and the Ultra-Violet and Optical
Telescope (UVOT; Roming et al., 2005) — which can search for the
electromagnetic counterparts to the _Swift_ Burst Alert Telescope (BAT;
Barthelmy et al., 2005) triggers. However, the _Fermi_ Gamma-ray Burst Monitor
(GBM; Meegan et al., 2009; von Kienlin et al., 2020) dominates the GRB
detection rate, finding $\sim 1$ per day, but with much larger location
uncertainties compared to _Swift_. Other than _Fermi_ -GBM, _Fermi_ also
equipped the Large Area Telescope (LAT; Atwood et al., 2009) in order to
detect high-energy gamma-ray emission from the GRB sources. The detection rate
of _Fermi_ -LAT is $\sim 10$ per year (Kumar & Zhang, 2015). As _Fermi_ does
not have either an X-ray or optical telescope on-board, and for GRBs for which
there is no joint _Swift_ detection, it is important to follow-up the _Fermi_
GRB detections in order to expand the sample of GRB afterglows available for
GRB studies.

In general, there are two observing strategies that are used to find GRB
optical afterglows: serendipitous and target-of-opportunity (ToO) follow-ups.
For instance, Andreoni et al. (2021) demonstrates how to identify
serendipitous fast transients, such as optical afterglow and kilonova,
detected by _Zwicky Transient Facility_ (ZTF) using ZTFReST, an automated
filtering and follow-up infrastructure. The greatest science return of using
this strategy is the proof of the existence of the orphan afterglow (Cenko et
al., 2015; Coughlin et al., 2020; Ho et al., 2020). However, it is not an
efficient way to searching for optical GRB afterglows as it is a blind search
of the sky (Nakar et al., 2002; Huang et al., 2020). On the other hand, ToO
follow-up directly searches for the optical counterparts of the detected GRB
by tiling skymaps generated by the _Fermi_ or _Swift_ instruments (Singer et
al., 2013, 2015; Coughlin et al., 2019; Ahumada et al., 2021). However, the
sizes of these skymaps can vary substantially, from square degrees to
arcseconds, depending on the gamma-ray instrument. Targeting potential host
galaxies and multi-color observations are usually used in ToO follow-ups,
which help to improve search efficiency and identify the origin of the
candidates. Other than ZTF, there are other observatories which actively
follow-up GRBs, such as Global MASTER-Net (Lipunov et al., 2012), Nordic
Optical Telescope (NOT; Djupvik & Andersen, 2010) and GROWTH-India Telescope
(GIT), DDOTI (Watson et al., 2016).

The Gravitational-wave Optical Transient Observer (GOTO) is an optical robotic
telescope that consisted of four 40 cm f/2.5 unit telescopes (UTs) in its
prototype design (GOTO-4) until 1 November 2019 and was upgraded to a full
eight UTs (GOTO-8) in November 2019 (Dyer et al., 2020b, Steeghs et. al in
prep). The primary objective of the GOTO project is to detect the optical
counterpart of gravitational-wave (GW) events detected by the LIGO-Virgo
collaboration (LVC) network. GOTO followed up LVC triggers distributed during
the third observing period, O3 (between April 2019 and March 2020), and the
details of GOTO’s O3 follow-up strategies and results are presented in
Gompertz et al. (2020). In the absence of active GW triggers, GOTO also
listens to automated alerts for GRBs from satellites such as _Fermi_ and
_Swift_. In the absence of any GRB or GW triggers, GOTO performs an all-sky
survey on a routine basis. The pixel scale of GOTO is $\approx 1.2$ arcsec per
pixel. GOTO can reach depths of $\sim$21 mag in the broad Baader L filter with
a co-added set of $4\times 90\,{\rm s}$ observations. Combined with a wide
field of view (FoV) of $\approx 40\,$square degrees in the GOTO-8 prototype
design, GOTO has the capability for searching for _Fermi_ GRB optical
counterparts.

In this paper we demonstrate how we perform automated follow-up and detail
strategies for how we narrow down the number of potential candidates of a
_Fermi_ -GRB optical afterglow. We also discuss the expected improvement in
our follow-up strategy for the current GOTO-8 and for forthcoming upgrades to
the network. In §2, we describe our current observing strategy and in §3 we
indicate how we filter the GRB events automatically. The flow of manual
filtering, which is different from the automated tasks from §3, in the final
stages is outlined in §4. Our final results are described in §5. Finally, we
discuss the planned expansion of the GOTO network and future follow-up
strategy in §6.

##  2 GOTO Observing Strategy for GRBs

GOTO is a fully-autonomous telescope and is controlled by the GOTO Telescope
Control System (G-TeCS; Dyer et al., 2018; Dyer et al., 2020a). The G-TeCS
software includes an alert monitor called the sentinel, which receives GW and
GRB alerts released through the NASA Gamma-ray Coordinates Network (GCN)
(Barthelmy et al., 1998). Once follow-up targets have been generated by GOTO
sentinel for an event they are added to the GOTO observation database from
which the automated scheduler will select targets and instruct the telescope
to move the mount to the requested position and take the requested exposures.
The entire system is automated and results in fast reaction times on minute
timescales; if the sky position is visible and GOTO is able to observe then
exposures can begin in $\sim$1-2 minutes of the alert being received. The fast
response of GOTO was successfully demonstrated by the follow-up observations
of GW events detected in the LIGO-Virgo collaboration (LVC) O3 run (Gompertz
et al., 2020).

When not following-up alerts GOTO carries out an all-sky survey based on a
fixed grid of tiles, which builds up an archive of reference images covering
all points on the sky. When a GW or GRB alert is received its probability
region is mapped onto the same grid as the survey, which allows any new images
to be compared to the reference templates taken at the same position (see
Section 3). Mapping the event skymap onto the survey grid is done using the
goto-tile Python package (Dyer, 2020).

For _Fermi_ GRB events, a two-dimensional Gaussian skymap is independently
created by goto-tile, centered at the location reported by a GCN. Since
_Fermi_ -GBM shows a systematic error of $\approx 3.6^{\circ}$ (at 68%
confidence level; Connaughton et al., 2015), we use the quadrature sum of the
systematic error and the statistical error (which is included in the GCN) as
the 68% confidence region of the skymap. The measurements of the GRB location
reported on GCN are only useful for generating our own Gaussian skymap as
there are delays of $\sim 10$ minutes between receiving the the initial alert
and the generation of the official _Fermi_ skymap. We will ultimately replace
the artificial Gaussian skymap with the official _Fermi_ skymap once it has
been received (see §6.1 for more details about the difference between our
Gaussian skymap and the _Fermi_ skymap).

Once the skymap has been created by goto-tile, the contained probability
within each GOTO tile is calculated. For this work, a large fraction of our
observing period overlapped with LIGO-Virgo O3. In order to avoid observations
taking excessive amounts of time away from completing our template set before
O3 and the follow-up observations of GW events during O3, only the five tiles
with the highest probability are added into the observation database and only
if they each include at least 5% of the overall localization probability error
region.

As well as determining which tiles to target for follow-up observations, the
G-TeCS sentinel also defines the number of times each tile should be observed
and the delay between observations. In order to confirm whether an observed
transient source is associated with the GRB at least two observations are
required within 1 day after the trigger, to confirm the fast-decay nature of
the GRB optical afterglow (Kann et al., 2010, 2011). Therefore, for GRB
observations the sentinel uses the strategy TWO_FIRST_ONE_SECOND, which
requires two observations to be taken within the first day after the trigger
followed by another single exposure the day after. It should be noted that
G-TeCS uses a “just-in-time” scheduling system, which while it is flexible
enough to allow for very fast initial observations, it cannot guarantee the
exact timings for subsequent observations. Even accounting for delays due to
poor weather or if the Sun rises before a second observation can be taken, it
is possible that a higher-priority target can be added into the scheduler
queue, taking precedence over the GRB target while both targets are visible.

Finally, when targets are added into the observations database, the exposure
sets are then similarly defined. For Fermi-GRB sources a set of four, 90
second exposures are taken using GOTO’s wide L filter (400-700 nm). In this
work, all GOTO magnitudes have been calibrated in the standard way as
described in Dyer et al. (2020b).

This work is an independent project of GOTO designed to test approaches for
GRB afterglow searches, which does not represent the GOTO standard filtering
procedures as described in Dyer et al. (2020b).

##  3 Data Preparation

###  3.1 Data Selection

In this paper, we outline the results of the GRB follow-up from 22 February
2019 to 7 June 2020. We used the GOTO-4 prototype configuration until 1
November 2019. Beyond that date, we used the upgraded to GOTO-8 prototype
configuration.

From 22 February 2019 to 7 June 2020, there were 508 _Fermi_ -GBM triggers
reported on _Fermi_ trigger GCN. Among those, there were 376 triggers located
at declination greater than $-30$ degrees. Due to further restrictions of the
GRB locations and timing and weather conditions at the site, GOTO observed a
total of 93 of these alerts. Since one of the alerts (TriggerNum: 596808579)
was later classified as a non-GRB trigger, we further reduce the observed
targets to 92. The GOTO response times range between $\approx 140$ seconds to
$\approx 3$ days, with the median response time $\approx 13$ hours (see Figure
1). There are three reasons which can greatly delay the GRB follow-up
observations. Firstly, bad weather or poor site conditions are the most common
issues preventing us from observing the event immediately after the trigger.
Secondly, the event location is not always observable when triggered. Finally,
since GW event triggers always have a higher follow-up priority, we do not
interrupt any ongoing follow-up observation of the GW event due to the GRB
trigger. Therefore, we postpone the GRB follow-up until the GW follow-up has
finished.

Figure 1: Cumulative distribution of GOTO response time for all 92 observed
_Fermi_ -GRB triggers. The response time has the range between 141 seconds and
70 hours. The median response time is 12.9 hours.

Motivated by the nature of expected GRB afterglow decay timescales (Kann et
al., 2010), we focus only on events for which observing commenced within 16
hours after the trigger. There are 58 out of 92 events fulfilling this
criterion. The objective of this work is to perform a systematic search for
optical counterparts to GRBs which were detected by solely by _Fermi_ -GBM. It
also helps to inform our future GW search strategies. Therefore, we filter out
5 events which have joint-detection with _Swift_ -BAT such that we have 53
_Fermi_ events in total. The details of all events followed up with GOTO are
shown in Table 3. It includes the event time and the location reported in GCN
of each GRB. We also include the response time of our first follow-up
observation after the trigger. The coverage percentages shown in Table 3 are
calculated based on the official skymap provided by _Fermi_. The expected
probability of detecting the optical afterglow for each GRB estimated base on
Eq. 3 is also included in Table 3.

###  3.2 Image Processing

The raw images are processed with the GOTO standard pipeline (Dyer et al.,
2020b), which includes bias correction, dark-frame subtraction and co-addition
of individual images. All images used to perform analyses in this paper are
co-added median science images.

A stacked template image of four individual exposures is used to perform image
subtraction. It acts as a reference image taken before the GRB trigger. The
set of templates are updated regularly by tiling the sky on a fixed grid, as
described in Section 2. We align the template to match with the science image
by using Python package spalipy111https://github.com/Lyalpha/spalipy. We use
hotpants (Becker, 2015) to perform image subtraction. Since not all fields
have templates taken before the science images, we use the last observation
prior to the GRB trigger as our reference image if the template does not
exist. In the image subtraction step, we generate 1229 difference images in
total for all 53 _Fermi_ -GRB events.

###  3.3 Filtering Processes

After the difference imaging process, we gather all source detections in the
difference images recovered by SExtractor (Bertin & Arnouts, 1996). Prior to
any filtering, there are 15 049 101 detections in total among the 1229
difference images. For those GRBs with $\approx 100\%$ coverage, the set of
images can cover more than the $1\sigma$ region of the skymap. However, since
the current observing strategy used is covering a fixed number of grids
instead of covering certain proportion of the skymap, we account for all the
detections in those difference images.

####  3.3.1 Real-bogus classification

After the image processing, we apply the real-bogus classification on the
difference images to separate the bogus detections and the real detections by
using supervised machine learning technique (Mong et al., 2020; Killestein et
al., 2021). We choose the decision boundary such that the upper limits of the
false positive rate and the missed detection rate are $2\%$ and $4\%$
respectively. After the real-bogus classification, there are 60 085 detections
which are classified as “real” on the difference images. All “real” detections
proceed to the next filtering step.

####  3.3.2 Bad data pre-filtering

Any detection that satisfies one of the following conditions is classified as
a bad detection or statistical noise;

  1. 1.

the physical position lies within 50 pixels from the edges (the image size of
GOTO is $8176\times 6132$ pixels with an angular resolution of $\approx 1.2$
arcsec per pixel),

  2. 2.

the full-width half-maximum (FWHM) of the detection on the difference image is
greater than the $95$th-percentile of the FWHM distribution of the science
image detections,

  3. 3.

the signal-to-noise ratio $<3\sigma$,

  4. 4.

the detection is fainter than the limiting magnitude of the science image,

  5. 5.

the detection is brighter than $14\,{\rm mag}$.

Of the 60 085 detections, 17 058 are classified as bad data or noise. Those
detections are then rejected from our candidate list in order to reduce the
time costs of cross-matching and human vetting process. Therefore, we further
reduce the number of potential candidates down to 43 027 by filtering the set
of “real” detections using image-based characteristics.

####  3.3.3 Catalog Cross-matching

Variable objects are commonly classified as real in the real-bogus
classification (see §3.3.1). To effectively reject the variables and the known
stellar objects from our candidates, we use Python package catsHTM (Soumagnac
& Ofek, 2018) to perform cross-matching with other public domain data of
stellar survey catalogs (see Table 1) including GAIA-DR2 (Gaia Collaboration
et al., 2018), 2MASS (Cutri et al., 2003), AAVSO (Watson et al., 2017), PS1
(Henden et al., 2015), UCAC4 (Chambers et al., 2016), IPHAS (Barentsen et al.,
2014) and SIMBAD (Wenger et al., 2000).

GRB optical afterglows are often found close ($\lesssim 10\,{\rm kpc}$) to
their host galaxy (Bloom et al., 2002; Fong & Berger, 2013; Blanchard et al.,
2016). A search for the presence of any known galaxy within 1 arcmin of the
detection can help us to prioritize those host-associated candidates.
Candidates with multiple nearby galaxies are prioritized first as they have a
higher chance of association with the GRB. With a matching radius of $10\,{\rm
kpc}$ (95–percentile of the GRB physical offset distribution; Blanchard et
al., 2016), 1 arcmin can cover down to $z\sim 0.008$, which is similar to the
redshift of the second closest GRB, GRB980425 (Tinney et al., 1998). For those
galaxies with known redshift, $z$, we can also estimate the isotropic
equivalent energy $E_{\rm iso}$ of the GRBs.

We use SIMBAD (Wenger et al., 2000) and the GLADE catalog (Dálya et al., 2018)
to perform galaxy cross-matching. SIMBAD provides reliable classification
based on the physical nature of the objects. The GLADE catalog is created by
combining four galaxy catalogs, GWGC, 2MPZ, 2MASS XSC and HyperLEDA, to
achieve a high completeness up to $\sim 40\,{\rm Mpc}$ (Dálya et al., 2018).
The completeness of the current galaxy catalogs is one of the main issue
throughout GRB follow-up studies. However, it cannot be resolved easily. There
are 2 095 out of 43 027 candidates found next to a known galaxy within 1
arcmin. We label all those candidates with near_galaxy=1, otherwise
near_galaxy=0.

Table 1: Catalogs used in cross-matching with our GRB-associated candidates. Catalog Name | Criteria | Reference
---|---|---
GAIA-DR2 | – | (1)
2MASS | – | (2)
AAVSO | – | (3)
APASS | – | (4)
PS1 | $0\geq\log|\mathcal{L}_{\rm ipsf}|>-3$ | (5)
| ${\tt iPSFMag}<19.5$ |
UCAC4 | ${\tt Yale\\_FLAG}=0$ | (6)
| ${\tt LEDA\\_FLAG}=0$ |
| ${\tt ExtCat\\_FLAG}=0$ |
| ${\tt 2MASSExt\\_FLAG}=0$ |
IPHAS | ${\tt mergedclass}=-1$ | (7)
| ${\tt pstar}>0.9$ |
SIMBAD | Non-Galaxy Types | (8)
(1) Gaia Collaboration et al. (2018) |
(2) Cutri et al. (2003) |
(3) Watson et al. (2017) |
(4) Henden et al. (2015) |
(5) Chambers et al. (2016) |
(6) Zacharias et al. (2013) |
(7) Barentsen et al. (2014) |
(8) Wenger et al. (2000) |

To determine whether a real detection on the difference image is associated
with a known stellar object from another catalog, we set a decision boundary
on the cross-matching offset. The average offset between the real detections
on the difference images and the known sources from other catalogs is:

$\displaystyle\theta=\sqrt{\theta_{\rm ds}^{2}+\theta_{\rm sc}^{2}}~{},$ (1)

where $\theta_{\rm ds}$ is the astrometric offset between the difference image
and the science image, and $\theta_{\rm sc}$ is the astrometric offset between
the science image and the catalog, respectively. Under the assumption that the
astrometry from GOTO gives $\theta_{\rm sc}\approx 0$, we have
$\theta\approx\theta_{\rm ds}$. Figure 2 shows the distributions of
$\theta_{\rm ds}$ and the angular separation between the detections on the
difference images and the second closest detections on the science images,
which they are presumably not associated with each other. We use the
95-percentile of $\theta_{\rm ds}$, which is at $\approx 6$ arcsec, to be our
decision boundary for claiming the association between the detection on the
difference image and the cross-matched source. However, from the orange
histogram in Figure 2, there are 0.7% real detections having at least one more
real detection within $6$ arcsec. Therefore, this filtering step might cause
$\approx 0.7\%$ false rejection rate.

We label all known stellar sources with known_source=1, otherwise
known_source=0. We then only reject those candidates with known_source=1 and
near_galaxy=0. This helps us to filter out those known stellar objects which
do not associate with known galaxy. With this filtering process, there are 12
568 candidates remain on our candidate list. Other than that, there could be a
possibility that some unresolved galaxies, which are not recorded in SIMBAD
and the GLADE, are misclassified as point sources in those stellar catalogs.
We cross-match the candidates rejected in this step with NASA/IPAC
Extragalactic Database222The NASA/IPAC Extragalactic Database (NED) is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration. (NED)
to obtain the misclassification rate as $\approx 0.2\%$, which is estimated by
the ratio between the number of the cross-matched galaxies in NED and the
total number of the known stellar sources.

Figure 2: Distribution of the angular separation between the detections on the
difference images and the two closest detections on the science images. The
blue histogram shows the distribution of the angular offsets of the closest
sources between the science images and the difference images due to the image
subtraction. The orange histogram shows the distribution of the angular
separation from the second closest, but unrelated, source.

####  3.3.4 Minor planet checking

We pass our remaining candidates to cross-match with the Minor Planet Catalog
(MPC) online333https://minorplanetcenter.net/. Any candidates with a known
cross-matched MP within $10$ arcsec at the observing epoch are rejected. There
are 10 126 detections remaining in our candidate list.

####  3.3.5 Multi-detection filtering

To further verify whether a detection is associated with the GRB or not, we
cross-match the detection with our source database. Following the same
procedure to perform cross-matching in §3.3.3, we associate the two cross-
matched detections within $6$ arcsec as the same detection.

Any candidates which have been recovered multiple times as real before the GRB
trigger or far beyond the triggering time should be excluded as they are not
associated with the GRB. Since GRB optical afterglows are fast transients
following a power-law decay

$\displaystyle F\propto t^{-\alpha}~{},$ (2)

where $F$ is the afterglow flux, $t$ is the time after the trigger and
$\alpha$ is the power-law index with a typical value of $\sim 1.2$ , we expect
that they become too faint to be detected in one to two days after the
trigger. However, as long GRBs are typically associated with supernovae, they
rise long after the optical afterglow has faded and show much longer decay
timescales in a few tens of days once the supernova has peaked in its emission
(Woosley et al., 1999; Klose et al., 2019). We define a GRB-associated period
as [$t_{0}$,$t_{0}+100$,days], where $t_{0}$ is the GRB trigger time. Any
candidates which have been recovered as real detections twice outside of the
GRB-associated period are rejected. Finally, we have 6 276 candidates left
after all the automatic filtering processes.

###  3.4 Summary of automatic filtering

In the automated filtering processes, we have filtered out about $90\%$ of the
real detections. The filtered detections include bad data (see §3.3.2 for the
definitions of bad data), known sources, minor planets and GRB-unrelated
sources.

##  4 Manual Filtering

###  4.1 Human vetting

After automatically filtering about $90\%$ of the real detections, we start
our vetting process by human inspection. Human vetting consists of three
steps, the manual real-bogus classification, the selection of the potential
GRB-related objects and the filtering of cosmic rays and bad data, which may
have inadvertently passed the automated stages.

The first step could be subjective. We suggest that different people review
each candidate multiple times to minimize subjective bias. In this work, we do
not take the issue of misclassification by humans into consideration.

For the second step, we select only those detections which satisfy either one
of the following criteria, there is a nearby galaxy within $10$ arcsec or it
does not exist on the template image. Since GRBs commonly show strong
association with their hosts, any detection found next to known galaxies could
be promising. The first criterion helps us to extract all detections with
small angular offset from a known galaxy. For those GRB sources having angular
offset $>10$ arcsec, they should be well separated from their host on the
image, which should be included with the second criterion. The second
criterion also includes any potential hostless GRB sources.

For the final step, we confirm that any candidate is not a cosmic ray by
verifying the existence of the detections on all individual images that make
up the median co-added science frame. For those detections which fall within
the overlapping region on multiple UTs, we also check to verify that the
detections are co-located in the overlapping UTs.

Under the human vetting process, there are 116 candidates passing the above
three steps. Among them, there are 55 candidates located within 1 arcmin from
at least one known galaxy registered in GLADE or SIMBAD.

###  4.2 Transient cross-matching

In this section, we describe our final filtering process. We cross-match each
potential candidate with the Lasair (Smith et al., 2019) and Transient Name
Server444https://wis-tns.weizmann.ac.il (TNS) candidate databases using their
API. Any candidates discovered before the GRB trigger epoch should not be
associated with the event. Therefore, we filter out all candidates which have
been discovered before the trigger. This step is separated from the catalog
cross-matching in §3.3.3 because catsHTM does not support the Lasair and the
TNS databases. Also, we do not loop our queries through their databases in
order to avoid overloading their servers.

In addition to the filtering according to the discovery epoch, we also filter
our candidates by their object types if their classification has been reported
by Lasair or TNS. The filtering process excludes the object types which are
very unlikely to be associated with the GRB optical counterpart, such as
variable stellar objects, type-Ia SN, or AGN. However, we have identified 2
candidates, ZTF18aaegvyd555https://lasair.roe.ac.uk/object/ZTF18aaegvyd/ and
ZTF18acaujfk666https://lasair.roe.ac.uk/object/ZTF18acaujfk/, which show re-
brightening within the first day after the trigger and do not have a confident
source classifications. We decide to keep those 2 candidates in our candidate
list for further photometric analysis. After the transient cross-matching, we
obtain a final list of 29 potential candidates.

Table 2: Number of candidates filtered at each step of transient vetting. Filtering step | Number of remaining candidates
---|---
| Before | After
Automated Filtering |  |
Real-bogus classification | 15 049 101 | 60 085
Bad data pre-filtering | 60 085 | 43 027
Catalog cross-matching | 43 027 | 12 568
Minor planet filtering | 12 568 | 10 126
Multi-detection filtering | 10 126 | 6 276
Manual Filtering |  |
Human vetting | 6 276 | 116
Transient cross-matching | 119 | 29

##  5 Results

There are 29 final candidates which passed through all the filtering
processes. In this section, we investigate the candidates primarily through
photometric measurements derived from forced photometry.

We also estimate the expected number of GRB optical afterglows which could be
detected for all those 53 GRB events.

###  5.1 Forced photometry Analysis

We use the forced photometry service provided by ZTF and
ATLAS777https://fallingstar-data.com/forcedphot/ to inspect the lightcurves of
all potential candidates. Any flux measurement with signal-to-noise ratio
(SNR) greater than $5\sigma$ is considered a detection. In order to avoid
treating any subtraction residual on the difference image as real detections,
we inspect all cutout images for those detections with ${\rm SNR}>5\sigma$.

Among those 29 candidates, there are 2 candidates $\gtrsim 10$ arcsec away
from known MPs, 4525 Johnbauer and 6384 Kervin. As we are unable to see any
detection from both ZTF and ATLAS forced photometry data, we conclude that
they are very likely minor planets. We generate the lightcurves for the
remaining 27 candidates between 365 days before the trigger and 365 days after
their trigger.

####  5.1.1 ZTF18aaegvyd/SN2019env

As mentioned in §4.2, ZTF18aaegvyd re-brightened in the first day of the GRB
triggers (see Figure 3). ZTF18aaegvyd was spectroscopically classified as a
Type-II SN (Smith et al., 2020), SN2019env888https://www.wis-
tns.org/object/2019env in TNS, at $z=0.0235$ by the Spectral Energy
Distribution Machine (SEDM) on the Palomar 60-inch telescope (P60). ATLAS
reported the first detection of the SN about 9 hours before the GRB was
triggered. Since Type-II SN is not a typical origin of GRB (Galama et al.,
1998; MacFadyen & Woosley, 1999; MacFadyen et al., 2001), also with the pre-
detection epoch which is inconsistent with the typical delay of the GRB-SN, we
conclude that SN2019env was not associated with the GRB event, Fermi578679393.

####  5.1.2 ZTF18acaujfk

ZTF18acaujfk is another transient discovered by ZTF which re-brightened on the
same day of the GRB trigger. However, the forced photometry data from ATLAS
shows that the re-brightening had started within 1 day before the trigger time
and the detection only lasted for one day (see Figure 3). The brightness of
the source seems to be stable during its active period. Due to the pre-
detection from ATLAS, ZTF18acaujfk is unlikely associated with the GRB.

ZTF18acaujfk does not show any detections between 242 days before the trigger
and 369 days after the trigger, except for the detection on the day of the
trigger. The first detection was claimed by ZTF on 9 October 2018 with
$g=18.3$, which was 245 days earlier than the trigger time. However, according
to the forced photometry data, it was first detected by ATLAS 33 days before
the source was discovered by ZTF. More interestingly, ZTF claimed another SN
detection at the same position 1 year after the GRB trigger. Since the typical
timescale of SNe is much shorter than a year, if the classification performed
by ZTF is correct (Smith et al., 2020), we expect that the source would be
unrelated to the other events at the same position. However, as this
classification has not been spectroscopically confirmed as a SN, we instead
interpret this signal as being more consistent with a quasi-periodic variable
source.

Cataclysmic variables (CVs) usually show a periodicity of several hours or
repeated high amplitude outbursts (Ritter & Kolb, 2003; Kalomeni et al.,
2016). Since ZTF18acaujfk was detected three times in around 2 year, it could
potentially be CV. For the galactic stellar flare, ZTF18acaujfk matches with
the typical active period of a few hours. However, it should consistently be
detected. We cannot confirm the transient type of ZTF18acaujfk solely by the
the available photometry due to its large variation of the decay timescale
from hours to days. In order to further verify the transient type of
ZTF18acaujfk, we need to obtain more data by further observations and through
spectroscopic classification.

Figure 3: Lightcuves of ZTF18aaegvyd/SN2019env (top) and ZTF18acaujfk
(bottom). The orange dashed line indicates the epoch of the GRB trigger. The
grey inverted triangles indicates the limiting magnitudes of ATLAS
observations. Both sources show re-brightening on the first day of the GRB
trigger.

####  5.1.3 Other GRB-unrelated transients

Among the remaining 25 candidates, 3 of them, which are labelled as known
sources from catalog cross-matching (see §3.3.3), are identified as variable
stellar objects from the characteristic variability of their lightcurves. They
initially passed our checks and are considered as candidates due to at least
one known galaxy within 1 arcmin around the source.

Figure 4: Lightcurves of the candidates which are identified as variable
stars.

We have also identified 2 unregistered variable sources. However, they show
periodicities of a few hundreds of days with a smooth variability which do not
look like typical variable stellar objects (Figure 5). In addition, ATLAS
shows that they are $\sim$2–4 magnitudes brighter in $o$-filter detection than
that in $c$-filter detection. It indicates that they are red in colour, which
match with the observational properties of Mira variables.

Figure 5: Lightcurves of two unregistered periodic transients. From their
periodicities and color, they are very likely to be Mira variables.

We found another 2 unknown transients, which are named as
GOTO103202.04-120240.18 and GOTO062359.85-185857.69, which showed pre-
detections before the triggers by ZTF and ATLAS, respectively (see Figure 6).

GOTO103202.04-120240.18 was detected by all three instruments, GOTO, ZTF and
ATLAS. However, since the first detection obtained by ZTF was around 5 days
before the GRB trigger, we conclude that GOTO103202.04-120240.18 was not
related to the GRB. From the lightcurve generated using 2-year forced
photometry data, the source only stayed active for $\approx 20$ days around
the GRB trigger. Also, it showed a relatively stable brightness over the
entire observing period except for the first ZTF $r$-band detection. We can
also see a faint extended source located at the position of
GOTO103202.04-120240.18 on Pan-STARRS images. Due to the gap between the 6th
and the 7th detections, and without any spectroscopic classification, we are
unable to confirm the nature of GOTO103202.04-120240.18.

GOTO062359.85-185857.69 was detected by ATLAS starting $\sim 250$ days before
the GRB trigger. We do not find any point-source appearing outside the active
periods of the source as observed by ATLAS on both ZTF and GOTO images.
However, we find a co-located source within archival Pan-STARRS images at the
same position of GOTO062359.85-185857.69. The source can be seen in $g$, $r$,
$i$ and $z$ bandpasses except $y$-band, which indicates the blue color of the
source. Due to the multiple detections from ATLAS and the existence of the
stellar source on Pan-STARRS images, it is unlikely to be associated with the
GRB. Nevertheless, limiting magnitudes of ATLAS observations in Figure 6 show
that the source was being monitored around the period of the GRB trigger,
which indicates that the re-activation of the source and the GRB triggering
epoch are temporally coincident.

Figure 6: Lightcurves of GOTO103202.04-120240.18 (top) and
GOTO062359.85-185857.69 (bottom). The orange dashed line indicates the epoch
of the GRB trigger. The grey inverted triangles indicates the limiting
magnitudes of ATLAS observations. Both of the sources were detected before the
GRB trigger times, which imply that they are unlikely to be related to the GRB
event.

####  5.1.4 Other potential candidates

For the remaining 18 candidates. we cannot draw any solid conclusion for them
due to the lack of observational data. However, we can still divide them into
3 groups according to similarities in their characteristics.

There are 6 candidates that fall into group 1: GOTO105852.27+491055.26,
GOTO175424.66+694237.24, GOTO175722.6+692716.7, GOTO175823.15+694250.58,
GOTO180217.26+695300.86 and GOTO190520.52+630533.28. All of these candidates
are within $2$ arcsec from the center of a galaxy. They were not detected by
either ZTF or ATLAS. As they are found with low spatial offsets from the
galaxies, the resulting sources on their subtracted images do not show clear
point-like structures. Therefore, at least another observation within the
first day after the trigger can help us to confirm the detection and constrain
the decay properties of the afterglow.

There are 7 candidates classified as group 2: GOTO064003.86+294644.32,
GOTO051809.33+222414.61, GOTO190511.9-260027.86, GOTO190642.62-211323.51,
GOTO191337.34-244759.56, GOTO192152.79-193955.67 and GOTO190259.23-243739.33.
Both ZTF and ATLAS have never shown any historical photometric detections of
these 7 candidates. Only a single detection or multiple detections taken at
the same time were obtained by GOTO for each of them. Therefore, we cannot
strongly constrain their lightcurves, including rise time and decay rate.
However, we can see a faint point-like object near each of the candidate
positions on the Pan-STARRS images. Given that they are stellar objects, these
candidates could be M-dwarf flares or GRB optical afterglows which are located
right next to a stellar object.

Group 3 involves 5 candidates: GOTO150228.81-080300.02,
GOTO091511.45-003731.96, GOTO190729.64-241429.03, GOTO191011.08-261449.76 and
GOTO211106.8-192555.33. Group 3 candidates and group 2 candidates share the
same features, except that we do not find any nearby objects on the Pan-STARRS
images. This difference makes the group 3 candidates the most interesting as
they are unlikely to be stellar objects (see their cutout thumbnails in Figure
7). However, there is still a possibility that they are unregistered MPs. To
confirm whether they are GRB optical afterglows, we need extra observations to
constraint their decay properties.

Figure 7: 70-by-70 pixel cutout thumbnails of the group 3 candidates. The
left, the middle and the right thumbnails are from the science image, the
reference image and the difference image, respectively.

To conclude, all candidates mentioned in this section could potentially be the
GRB optical afterglow, or other transient types. However, we do not have
sufficient data to further confirm their origins.

In our future follow-ups and based on our results, all candidates which pass
all of the filtering processes are deemed likely to be associated with the GRB
event and deserve extra follow-up. To do this, we need to improve the latency
at all stages of our vetting procedures in order to trigger spectroscopy with
other facilities nearby. The GRB association can further be confirmed if we
obtain a power-law spectrum. Also, extra observations on an identified host
galaxy can help to constrain physical properties of the system, such as the
star formation rate, metallicity, age, redshift and spatial offsets between
the host galaxy and the transient. These observables can help us to identify
and improve the confidence of the progenitor origin of the candidate.

###  5.2 Expected number of candidates

The probability of detecting an optical afterglow to a GRB event by GOTO can
be estimated by using

$\displaystyle P_{\rm OA}=P_{\rm cov}\cdot(1-P_{\rm dark})\cdot P_{m<m_{\rm
lim}}(t_{\rm obs},\theta_{\rm obs})~{}.$ (3)

The probability $P_{\rm cov}$ of covering the GRB position is simply the total
coverage of the official _Fermi_ healpix skymap. The term $P_{\rm dark}$ is
the “dark” GRB rate, which is assumed to be the lower limit of $0.4$ in our
estimation (Greiner et al., 2011). $P_{m<m_{\rm lim}}(t_{\rm obs})$ is the
probability that the optical afterglow is bright enough to be detected with
the an observing angle $\theta_{\rm obs}$ at $t_{\rm obs}$. The observing
conditions will affect the image quality and the limiting magnitude of our
observations, which could affect the probability of detecting a transient.
However, in our probability estimation, we do not take the observing
conditions into account.

We simulate 14 302 afterglow lightcurves with a power-law temporal decay
$F\propto t^{-1.2}$ using different combination of redshift $z$ and the
corrected magnitude $m_{0}(z=1,t=86\,{\rm s})$. The samples of $z$ and $m_{0}$
are drawn from the distributions presented in Zitouni et al. (2018) and Kann
et al. (2010). The simulated lightcurve with 1-$\sigma$ confidence region is
shown in Figure 8. We can obtain $P_{m<m_{\rm lim}}(t_{\rm obs})$ using the
simulated lightcurve (see Figure 9). Here, we assume that $\theta_{\rm
obs}\approx 0$. With the Eq. 3, the $P_{\rm OA}$ for each GRB event is shown
in Table 3.

The total expected number of optical afterglows is estimated as the sum of
$P_{\rm OA}$ for all events. For our sample of 53 events, we expect to detect
$\lesssim 3$ afterglows as the upper limit since we do not take the weather
conditions into account.

Figure 8: Simulated lightcurve of GRB optical afterglow following power-law
decay $t^{-1.2}$. The shaded region indicates the 1-$\sigma$ confidence level.
Figure 9: Probability $P_{m<m_{\rm lim}}$ of detecting an optical afterglow
brighter than $m=20$ as a function of observing time $t_{\rm obs}$, assuming
that the GRB is not dark and that GOTO covers the GRB location at $t_{\rm
obs}$.

##  6 Discussion and Improvements

In Eq. 3, the factors $P_{\rm dark}$ and $P_{m<m_{\rm lim}}$ depend on the
observational properties of the GRB and the limitation of the telescope, which
cannot be improved manually. However, the coverage $P_{\rm cov}$ can be
improved by optimising the observing strategy and with the addition of more
telescopes.

###  6.1 Gaussian skymap against official skymap

The skymaps used for tiling in our current GRB follow-ups are created
independently using a two-dimensional normal distribution. The distribution is
centered at the GRB position reported by the _Fermi_ -GBM with the confidence
region of the quadrature sum between the statistical error and the systematic
error (3.61 degrees; Connaughton et al., 2015).

The advantage of using manually-created skymaps is to minimize the follow-up
response time. The final version of the official skymaps published by _Fermi_
have a median delay time of $\sim 600\,{\rm s}$. Since the GRB optical
afterglow has a fast temporal decay (see the simulated lightcurve in Figure
8), the early post-trigger phase is the essential period for detecting the
afterglow emission. If we start follow-up observations after the _Fermi_
skymap is released, and assuming that we can cover the correct position within
the first 10 minutes, then $\sim 30\%$ of the GRBs would become too faint to
be detected under GOTO limiting magnitude of 20 (see Figure 9).

On the other hand, the official skymap generated by _Fermi_ -GBM provides a
more precise localization for the GRB detection. Our generated Gaussian
skymaps do not always cover the highest confidence region of the official
skymap. The similarity of the two skymaps can be measured by using the
overlapping index (Pastore & Calcagnì, 2019)

$\displaystyle\eta(f,g)=\oint\min[f(\mathbf{r}),g(\mathbf{r})]\,d\Omega~{},$
(4)

where $f$ and $g$ are the probability distributions of the two skymaps. The
index $\eta$ closer to 1 implies higher similarity between two skymaps. Figure
10 shows that the median value of $\eta$ is 0.75 for all 53 events, which
implies that the Gaussian and the official skymaps usually share reasonable
amount of overlapping portion. We also show two skymap tiling examples with
$\eta=0.87$ (Trigger ID: 593536021) and $\eta=0.53$ (Trigger ID: 578679393) in
Figure 11 to illustrate how $\eta$ affects the tiling of the skymap.

Figure 10: Histogram of the overlapping indices $\eta$ for all 53 _Fermi_ -GBM
GRB events. The orange and the blue histograms represent the skymap created by
using the systematic errors of 3.61 and 5.60 degrees, respectively. By
optimizing for the systematic error, the median value of $\eta$ has been
improved from 0.75 to 0.82.

Since we start our observations from the portion of the skymap with the
highest probability, we have to confirm that the peaks between our Gaussian
skymap and the official skymap do not deviate from each other by more than the
size of a single tile (FoV$\approx$20 square degrees). Figure 12 shows that
most of the offsets are consistent to within 3 degrees. Therefore, the offset
between the two skymaps is smaller than the size of a single sky grid.

Other than the offset, the Gaussian skymap should ideally be the same size as
the official skymap. If we use the systematic error of $3.61$ degrees to
create the intermediary Gaussian skymaps, most of will be smaller in extent
than the official ones (see Figure 13), which implies that we have
underestimated the systematic error. In order to generate a Gaussian skymap
with a similar size of the official one, we increase the systematic error to
maximize the likelihood function

$\displaystyle\log\mathcal{L}(\varepsilon_{\rm
sys})=-\frac{1}{2}\sum_{i=1}^{n}\left[\frac{x_{i}-y_{i}(\varepsilon_{\rm
sys})}{\sigma_{i}}\right]^{2}~{},$ (5)

where $x_{i}$ is the number of pixels on the Healpix grid (Górski et al.,
2005), which is a pixelization algorithm of 2-sphere with equal area for each
individual grid, of order=NESTED as defined by the Fermi skymap and
$y_{i}(\varepsilon_{\rm sys})$ is the number of Healpix pixels on the Gaussian
skymap generated with a systematic error $\varepsilon_{\rm sys}$. We apply
$\sigma_{i}=\sqrt{x_{i}}$ in the likelihood. The optimal value of
$\varepsilon_{\rm sys}$ is 5.6 degrees. With the optimal $\varepsilon_{\rm
sys}$, the median value of $\eta$ increases from 0.75 to 0.82 (see Figure 10),
which indicates that the overall similarity between the Gaussian skymap and
the official skymap has been improved.

Despite the high $\eta$, the official skymap cannot be reproduced perfectly by
a simple two-dimensional Gaussian distribution. To solve this problem, the
manually created Gaussian skymap will be replaced by the official skymap once
it is published, and the typical creation time of the official skymap is
$\approx 10\,{\rm mins}$. The observation schedule will then be updated in
response.

Figure 11: Examples of skymap tiling. The blue area represents the official
skymap and the orange grids represent the observed tiles generated based on
the Gaussian skymap. The top skymap shows a good tiling case. On the other
hand, the observed tiles on the bottom skymap shows a significant deviation
from the center of the skymap.

###  6.2 Tiling strategy

The size of the official skymaps shows a wide range of variation depending on
the uncertainty of the _Fermi_ -GBM localization. Even with a high visibility
for some events (see Table 3), the coverages within 16 hours are still low,
which indicates that only covering the top five tiles is not enough in our
follow-up observations. The median size of the official skymap at $1\sigma$
confidence level is $\approx 150$ square degrees. With the GOTO protoype FoV
of $20$ square degrees, we need at least 8 tiles to cover 68% of the skymap.

The solution to this problem is straight forward. Instead of tiling a fixed
number of tiles, we should tile a fraction, e.g. 68%, of the skymap. With this
strategy, we can guarantee to cover a reasonable portion of the skymap even
with a large uncertainty. However, with this strategy, we require that a
minimum fraction, say 68%, of the skymap can be covered within a certain
amount of time. The time constraint should not be set for too long due to the
fast-decay nature of the afterglow. According to Figure 9, we estimate that
80% of the afterglows would fall below the limiting magnitude of GOTO within
2.8 hours.

Figure 12: Offset between the peaks of the Gaussian skymap and the official
skymap against the _Fermi_ reported statistical error. The offsets mostly lie
within 3 degrees and shows no correlation with the statistical error. Figure
13: Correlation between the numbers of healpix pixels on the Gaussian skymap
(with the systematic error of 3.61 degrees) and the official skymap at
$1\sigma$ confidence level. The red line indicates the number of healpix
pixels on both skymaps are equal. Most of the data points lie below the red
line indicating the systematic error is underestimated.

###  6.3 Follow-up Cadence

With the current configuration of GOTO, it takes $4\times 90$ seconds of
exposure per each frame. Based on our 5-tile observing strategy, it takes 30
minutes to complete the whole tiling process. Figure 8 shows that GRB optical
afterglow can decay up to $\sim 10$ mag within the first 30 minutes after the
trigger.

In order to verify the fast-decay nature of GRB optical afterglows, if we can
trigger the first follow-up observation within 30 minutes after the trigger,
we should start our second follow-up observation immediately afterwards. Since
the afterglow decay follows the power-law function, the magnitude should decay
much slower on the linear timescale after the first hour of the trigger. To
estimate a proper cadence of the following observations, we use

$\displaystyle\Delta m=-2.5\log\left(\frac{t}{t_{0}}\right)^{-\alpha}~{},$ (6)

where $\Delta m$ is the magnitude difference between time $t$ and $t_{0}$. By
taking $\Delta m=1$ and $\alpha=1.2$, we obtain $t\approx 3.3t_{0}$, which is
our estimate of the cadence for the subsequent observation following the first
observation taken at time $t_{0}$.

##  7 Conclusion

From February 2019 to June 2020, the GOTO prototype followed-up 93 GRBs
detected by _Fermi_ -GBM. We conduct an archival search on 53 of the them
followed up within 16 hours and without _Swift_ joint detections.

We have developed a process to effectively filter detections that are unlikely
to be related to a GRB. We divide the process into two parts, automated and
manual. The automated process involves real-bogus classification, bad data
pre-filtering, catalog cross-matching, minor planet checking and multi-
detection filtering. These automated processes narrow down our candidate
number from 60 085 to 6 276. The manual filtering process involves human
vetting, transient cross-matching and forced photometry analysis. In the human
vetting step, we finally obtain 119 transient-like objects, 55 of which have
nearby galaxies. Transient cross-matching further helps us filter out some
GRB-unrelated sources, ultimately resulting in 29 potential candidates.

We apply forced photometry on those 29 candidates using data obtained by GOTO,
ZTF and ATLAS. We analyze their lightcurves and find that 11 of them are
unlikely to be related to any GRB. For the rest of the candidates, they can
potentially be associated as a GRB afterglow. However, we do not have enough
data to solidly constrain their transient types.

We expect to detect $\approx 3$ GRB optical afterglows among those 53 events.
The estimation is calculated by simulating the lightcurve of the afterglow.
The skymap coverage of each event and the dark GRB rate are also considered in
the calculation.

In order to improve our performance, we recommend using 5.6 degrees as the
systematic error to create a Gaussian skymap for tiling before the official
skymap provided by _Fermi_ is released. Once the official skymap is released,
which should take $\sim 10$ minutes after the trigger, we should use this
updated skymap for tiling. For the tiling strategy, we should image at least
$1\sigma$ of the visible skymap to ensure that a reasonable portion of the
skymap is covered. If the first follow-up observation can be triggered within
30 minutes after the GRB alert, we also recommend multiple observations. In
order to verify the nature of fast decay, a second follow-up should be
performed immediately following the first one.

## Acknowledgements

We thank the referee, Michael Coughlin for the comments that improved this
paper. The Gravitational-wave Optical Transient Observer (GOTO) project
acknowledges the support of the Monash-Warwick Alliance; Warwick University;
Monash University; Sheffield University; University of Leicester; Armagh
Observatory & Planetarium; the National Astronomical Research Institute of
Thailand (NARIT); the Instituto de Astrofísica de Canarias (IAC) and the
University of Turku. RLCS and POB acknowledge support from STFC. RB, MK and
DMS acknowledge support from the ERC under the European Union’s Horizon 2020
research and innovation programme (grant agreement No. 715051; Spiders). VSD
and MJD acknowledge the support of a Leverhulme Trust Research Project Grant.

## Data availability

Data files covering the system throughput and some of the software packages
are available via public github repositories under https://github.com/GOTO-
OBS/. Prototype data was mainly used for testing and commissioning and a full
release of all data is not foreseen. Some data products will be available as
part of planned GOTO public data releases.

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Table 3: _Fermi_ -GRB event table. Trigger Number | Event Time | R.A. | Dec. | Error | Response | Skymap Coverage / | Expected
---|---|---|---|---|---|---|---
|  |  |  |  | Time | Visibilitya | Probabilityb
| (UTC) | (hh:mm:ss) | (dd:mm:ss) | (Deg.) | (Hrs) | (%) | (%)
572876510 | 2019-02-26T12:21:46 | 14:57:43.2 | -08:36:36 | 5.11 | 13.911 | 23.6/87.2 | 1.2
573284727 | 2019-03-03T05:45:22 | 19:55:48 | +29:51:00 | 23.97 | 0.476 | 22.7/60.7 | 7.2
573604668 | 2019-03-06T22:37:43 | 15:24:16.8 | -00:22:48 | 2.55 | 0.0392 | 87.3/100 | 45.2
574345067 | 2019-03-15T12:17:42 | 09:46:14.4 | -11:09:00 | 2.11 | 8.146 | 71.8/100 | 5.2
574676902 | 2019-03-19T08:28:18 | 12:50:24 | -04:48:36 | 3.26 | 14.373 | 100/100 | 5.0
575018216 | 2019-03-23T07:16:52 | 09:28:16.8 | +02:50:24 | 2.07 | 13.478 | 60.9/100 | 3.2
576241792 | 2019-04-06T11:09:47 | 19:05:21.6 | +61:30:00 | 7.09 | 14.557 | 32.5/96.5 | 1.6
576265958 | 2019-04-06T17:52:33 | 19:30:33.6 | +26:47:24 | 5.46 | 9.077 | 19.3/100 | 1.3
578252995 | 2019-04-29T17:49:51 | 13:20:12 | -08:00:00 | 8.00 | 3.121 | 3.7/99.8 | 0.4
578679393 | 2019-05-04T16:16:28 | 09:13:57.6 | +28:41:24 | 9.61 | 5.045 | 17.9/99.8 | 1.7
578711654 | 2019-05-05T01:14:09 | 22:21:33.6 | +42:10:48 | 9.54 | 2.391 | 10.5/82.8 | 1.4
578903308 | 2019-05-07T06:28:23 | 10:23:50.4 | -12:48:00 | 4.82 | 14.583 | 53.0/99.6 | 2.6
578963794 | 2019-05-07T23:16:30 | 19:11:16.8 | -22:49:12 | 1.19 | 3.567 | 54.2/93.8 | 5.9
579036175 | 2019-05-08T19:22:50 | 11:51:50.4 | +23:31:48 | 2.12 | 1.688 | 17.1/100 | 2.8
579814215 | 2019-05-17T19:30:10 | 18:00:04.8 | +25:46:12 | 1.20 | 3.250 | 77.7/100 | 9.1
580437952 | 2019-05-25T00:45:48 | 22:32:04.8 | +05:27:00 | 4.04 | 2.712 | 12.7/86.5 | 1.6
580904353 | 2019-05-30T10:19:08 | 08:03:02.4 | +35:30:00 | 10.20 | 11.028 | 25.3/30.8 | 1.5
581068049 | 2019-06-01T07:47:24 | 10:51:55.2 | +54:35:24 | 8.28 | 13.581 | 25.3/99.8 | 1.3
581281470 | 2019-06-03T19:04:26 | 01:20:19.2 | +40:54:36 | 5.86 | 9.579 | 13.0/30.8 | 0.9
581337762 | 2019-06-04T10:42:37 | 22:50:12 | +46:22:12 | 1.00 | 14.974 | 51.5/54.5 | 2.5
581469752 | 2019-06-05T23:22:27 | 22:28:57.6 | +04:47:24 | 6.76 | 3.691 | 9.5/100 | 1.0
581882394 | 2019-06-10T17:59:50 | 21:49:31.2 | +42:25:12 | 1.21 | 6.603 | 50.2/100 | 4.0
581889628 | 2019-06-10T20:00:24 | 20:59:19.2 | -15:55:48 | 11.23 | 5.798 | 8.1/92.7 | 0.7
582004649 | 2019-06-12T03:57:25 | 14:55:48 | +62:06:00 | 9.30 | 0.190 | 10.1/61.3 | 4.1
582304592 | 2019-06-15T15:16:27 | 12:45:36 | +49:22:48 | 2.32 | 6.748 | 47.0/100 | 3.7
582596766 | 2019-06-19T00:26:02 | 23:17:14.4 | +12:51:36 | 2.05 | 1.916 | 50.4/100 | 7.8
582725415 | 2019-06-20T12:10:11 | 10:48:19.2 | +30:28:48 | 1.16 | 9.348 | 100/100 | 6.7
584590606 | 2019-07-12T02:16:42 | 19:13:33.6 | +56:09:00 | 7.59 | 0.186 | 13.3/100 | 5.5
585007213 | 2019-07-16T22:00:08 | 23:02:31.2 | -00:49:48 | 6.43 | 2.811 | 0.02/100 | 0
585559462 | 2019-07-23T07:24:18 | 19:17:52.8 | +25:13:12 | 10.47 | 13.988 | 5.9/100 | 0.3
585847498 | 2019-07-26T15:24:54 | 20:41:02.4 | +34:17:24 | 1.17 | 5.944 | 100/100 | 8.5
592297741 | 2019-10-09T07:08:57 | 01:47:14.4 | +65:43:48 | 1.41 | 12.773 | 97.6/100 | 5.4
593045905 | 2019-10-17T22:58:21 | 08:58:12 | +15:19:48 | 12.39 | 5.196 | 0.7/99.8 | 0.1
593176520 | 2019-10-19T11:15:15 | 07:18:14.4 | +62:05:24 | 3.28 | 13.831 | 19.6/93.2 | 1.0
593419810 | 2019-10-22T06:50:05 | 18:12:33.6 | -23:06:00 | 3.18 | 12.870 | 21.1/22.1 | 1.1
593536021 | 2019-10-23T15:06:57 | 19:41:02.4 | +06:10:48 | 1.82 | 4.573 | 73.0/100 | 7.2
593928606 | 2019-10-28T04:10:01 | 21:16:48 | -11:17:24 | 8.75 | 15.459 | 20.0/99.6 | 0.9
593964489 | 2019-10-28T14:08:04 | 18:27:31.2 | +69:59:24 | 7.67 | 6.0339 | 49.2/97.8 | 4.2
596387570 | 2019-11-25T15:12:46 | 23:34:09.6 | +18:12:00 | 4.13 | 4.207 | 38.3/100 | 3.9
596786686 | 2019-11-30T06:04:41 | 23:17:36 | +63:04:48 | 2.27 | 14.151 | 35.4/99.9 | 1.8
Trigger Number | Event Time | R.A. | Dec. | Error | Response | Skymap Coverage / | Expected
---|---|---|---|---|---|---|---
|  |  |  |  | Time | Visibilitya | Probabilityb
| (UTC) | (Deg.) | (Deg.) | (Deg.) | (Hrs) | (%) | (%)
597955752 | 2019-12-13T18:49:08 | 22:04:14.4 | -13:56:24 | 6.67 | 0.665 | 36.0/94.3 | 14.0
598951521 | 2019-12-25T07:25:17 | 06:21:57.6 | -17:21:00 | 6.66 | 15.246 | 35.7/82.3 | 2.2
598988276 | 2019-12-25T17:37:52 | 09:43:12 | -07:10:48 | 2.84 | 7.410 | 100/100 | 7.6
600448273 | 2020-01-11T15:11:08 | 06:57:57.6 | +31:43:12 | 3.47 | 11.244 | 88.6/100 | 5.9
600525396 | 2020-01-12T12:36:31 | 10:00:31.2 | +64:24:36 | 2.00 | 9.431 | 90.3/100 | 6.5
601677816 | 2020-01-25T20:43:31 | 00:29:48 | +64:41:24 | 1.00 | 0.202 | 100/100 | 40.6
601841483 | 2020-01-27T18:11:19 | 05:03:33.6 | +20:04:12 | 3.26 | 1.740 | 45.5/100 | 11.8
603142206 | 2020-02-11T19:30:01 | 07:24:33.6 | +59:00:36 | 10.89 | 0.741 | 17.1/99.8 | 6.4
603849435 | 2020-02-19T23:57:10 | 17:37:55.2 | +08:23:24 | 1.00 | 4.818 | 87.5/100 | 9.6
610450873 | 2020-05-06T09:41:09 | 12:43:40.8 | +40:14:24 | 3.47 | 12.422 | 7.2/100 | 0.5
610800081 | 2020-05-10T10:41:17 | 10:20:19.2 | -01:55:48 | 1.50 | 10.659 | 63.7/100 | 5.8
611434353 | 2020-05-17T18:52:28 | 07:40:48 | +29:25:48 | 7.06 | 2.329 | 6.1/95.3 | 2.0
613212114 | 2020-06-07T08:41:50 | 11:26:00 | +30:52:48 | 2.10 | 12.744 | 67.0/100 | 4.1
a Calculated with the time constraints of 16 hours after the trigger. Official
_Fermi_ skymap is used.
b The probability of detecting the GRB optical afterglow estimated base on Eq.
3.