Detecting the Early Optical Flashes of Gamma-Ray Bursts with Small Telescope Arrays

We present an observational approach for the independent detection of the early optical emission of long gamma-ray bursts (GRBs). For this purpose, we explore the potential of the Large Array Survey Telescope (LAST). This array of small optical telescopes can be used to scan a wide region of the sky, and to focus on a smaller field of view with increased sensitivity, as needed. The modularity of the array facilitates dynamic scanning of multiple fields, by shifting telescope pointing directions with high cadence. This can significantly increase the effective sky-coverage of a blind survey on short timescales. For events associated with gamma-ray counterparts, the valuable early time data can supplement high-energy observations. Regardless of gamma-ray association, detections can potentially be used to explore various phenomena associated with GRBs, such as orphan afterglows; dirty fireballs; and choked jets. We simulate a sample of GRBs and their respective optical signals at early times. After accounting for dynamic cadence, the light curves are given as input to a machine-learning classifier, used to identify astrophysical transients. We find that, by dedicating half of an LAST array to a blind search, one would expect to independently detect 7–11 GRBs yr–1, corresponding to an approximate intrinsic event rate of 0.12 deg–2 yr–1.


INTRODUCTION
Gamma-ray bursts (GRBs) are the most luminous extragalactic sources in the Universe.They are caused either by the merging of two compact objects (e.g., neutron stars), or by the core-collapse supernovae (SNe) of massive stripped-envelope stars (Kumar & Zhang 2015;Woosley 1993;Eichler et al. 1989).Historically, the two scenarios have respectively been linked to shortand long-duration GRBs.These event-classes respectively exhibit prompt emission phases, which are typically shorter or longer than ∼ 2 sec.The prompt stage is followed by an extended afterglow phase.Thousands of GRBs have been detected to date.However, the exact mechanism of energy dissipation and the associated radiation processes remain an open question.
During the prompt stage of an event, over 10 51 erg of energy is released as γ-rays.This is thought to be produced by a relativistic jet that is launched by the central engine of the GRB.The jet is a collimated outflow of plasma, having an initial Lorentz factor, Γ init ≫ 100.The nature of the central engine is unknown, though it has been hypothesised to be an accreting black hole or a millisecond magnetar (Rees & Meszaros 1994;Thompson 1994).
At later times, a fraction of the energy of the jet is transformed to nonthermal radiation as part of the afiftach.sadeh@desy.deterglow.As the GRB outflow sweeps through the external circumburst medium, it is decelerated by a reverse shock, while a strong relativistic forward shock propagates outwards.The latter powers a long-lived emission, which is usually attributed to synchrotron radiation.It is detectable from radio to X-ray wavelengths on timescales of minutes to years (Mészáros & Rees 1997).
The focus of this work is long GRBs.Long GRBs are predominantly discovered via their prompt emission with dedicated high-energy (HE) X-ray/γ-ray satellites.In a handful of cases, GRBs have independently been detected via their prompt optical emission.Notable examples include those of GRB 080319B (Racusin et al. 2008) and GRB 130427A (Vestrand et al. 2014).However, most events are only observed in the optical band as part of multiwavelength (MWL) follow-up of HE signals.Follow-up campaigns involve many instruments, which are mainly ground based.These range from the radio band to very-high-energy (VHE) gamma-rays.The time lag involved in responding to GRB triggers from satellites is generally of the order of tens of sec.Follow-up is therefore mostly restricted to the afterglow phase of the emission, baring extreme luck, or the availability of very-wide-field instruments (Xin et al. 2023)).While very illuminating in itself, the afterglow in most cases is only indirectly tied to the prompt activity.This poses major challenges to our understanding of the underlying central engine.
The effective issuance of scientific alerts, e.g., via the General Circulars Network (GCN), 1 has greatly advanced the field.Alerts allow rapid response by robotic optical instruments (e.g., Steele et al. (2004); Klotz et al. (2009)); these facilitate MWL observation of GRBs in temporal coincidence with their prompt γ-ray emission (Yost et al. 2007a).Such observations have been used to investigate the relativistic jet while the central engine was still active, leading to a variety of interpretations.In some cases, optical flashes were attributed to internal processes, probing the engine (prompt emission); in others, they pointed towards external origins (afterglow emission), e.g., a reverse shock (Kopač et al. 2013;Troja et al. 2017;Zhang et al. 2018;Becerra et al. 2021;Xin et al. 2023;Oganesyan et al. 2023).
Fundamentally, early MWL data may do more than simply supplement our observations of the prompt γrays.In fact, some GRBs do not have an HE counterpart at all.Such nondetections can come about in different ways, the leading explanations being the following: (i) unobserved standard GRBs; (ii) orphan afterglows; (iii) dirty fireballs; and (iv) choked jets.We discuss each category in the following.
Standard GRBs may be missed due to lack of HE sky coverage and incomplete duty cycles.For example, Cenko et al. (2013) estimate that for events with fluence, F γ < 6 • 10 −7 erg cm −2 , there is a 40% chance of nondetection by the more sensitive instruments, Fermi-GBM (Meegan et al. 2009) and Swift-BAT (Gehrels et al. 2004).
Orphan events may lack HE counterparts due to viewing-angle effects, given that GRB jets are highly collimated.To illustrate the point, the local intrinsic volumetric rate of GRBs is 79 +57 −33 Gpc −3 yr −1 (Ghirlanda & Salvaterra 2022).On the other hand, the corresponding observed rate is 1.3 +0.6  −0.7 Gpc −3 yr −1 (Wanderman & Piran 2010).Most events are undetectable in HEs, as the prompt emission is beamed away from our line of sight.The MWL afterglow may nonetheless become visible, as the jet decelerates and expands sideways.Prompt low-energy emission may also be observable for on-axis structured jets that are undetected in γ-rays (Granot & Ramirez-Ruiz 2010).In such cases it is assumed that the relativistic jet is initially observable; however, it only contains a narrow core of high Lorentz factor, which emits all γ-rays beyond our line of sight.
Dirty fireballs are a hypothesized class of long GRBs with low Lorentz factors, 1 < Γ init ≪ 100.They are believed to be the result of high contents of baryonic mate- 1 The GCN, https://gcn.nasa.gov/circulars.rial entrained in the GRB jet (Piran 2004).These events are still expected to produce optical signals resembling long GRBs.However, their HE prompt emission might be entirely suppressed (Huang et al. 2002).Alternatively, if it exists, the prompt signal would peak below the nominal sensitivity window of γ-ray instruments.Such events go undetected in most cases, though they might appear as X-ray flashes (Heise 2003;Sakamoto et al. 2005) or as low-luminosity GRBs (Cano et al. 2017).
Choked jets & shock breakouts fall under another postulated scenario, where a mildly relativistic jet does not manage to successfully penetrate the stellar envelope (Waxman & Katz 2017).The failed jet dissipates all of its energy into the surrounding cocoon, driving it to expand.As the cocoon reaches the edge of the star, a mild-to-ultrarelativistic forward shock emits an X-ray/UV flash as it breaks out.This is followed by an extended UV/optical signal, arising from the expanding cooling envelope.These shock breakouts have also been associated with low-luminosity GRBs.However, as indicated, the origins and phenomenology of the prompt emission are distinct from jetted GRBs (Bromberg et al. 2011).
Studying each of the classes of "nonstandard" GRBs can shed light on fundamental questions in the field.For instance, while GRBs are disfavoured as the primary sources of ultra-high-energy cosmic rays (UHECRs) and high-energy cosmic neutrinos, they may still contribute to these phenomena under some conditions (Senno et al. 2016;Rudolph et al. 2022Rudolph et al. , 2023)).Leading uncertainties relate to determining realistic values for the baryonic loading; the location of the dissipation region; specifics of the radiation mechanisms; the structure of relativistic jets; the dividing line between successful and failed GRBs; and the true cosmological rate of events.These questions are closely tied to the connection between GRBs and SNe.Specifically relevant are SNe Ic-BL (core-collapse SNe with broad lines).These are stripped-envelope SNe having systematically high velocities in their optical spectra (compared to ordinary SNe Ic at similar epochs).SNe Ic-BL have decisively been associated with GRBs (Woosley & Bloom 2006).Determining the comparative rates between SNe and (low-luminosity) GRBs, in line with the respective dissipation/radiation models, will help us understand the physics behind massive stellar deaths (Ho et al. 2020;Corsi et al. 2023).
A promising direction to make progress on these topics is to increase the number of early time detections of GRBs in the optical band.This can be accomplished by performing a blind search with a wide-filed-of-view (FoV) telescope, circumventing the need for satellitetriggers.If available, detections could be connected after the fact to HE and VHE counterparts, enabling studies of the prompt emission spectra (Oganesyan et al. 2019).A connection could also be made to possible shock breakout signals via e.g., the upcoming ULTRA-SAT satellite (Shvartzvald et al. 2023).At later times, events would possibly be associated with SNe via deep optical and radio follow-up, as well as to VHE neutrinos.
Multiple groups have attempted to independently detect GRBs and other short transients in the optical band (Ho et al. 2018;van Roestel et al. 2019;Andreoni et al. 2020a;Arimatsu et al. 2021;Berger et al. 2013).For example, the Robotic Optical Transient Search Experiment-III (ROTSE-III) conducted a search over a FoV of 3.4 deg 2 with an effective limiting magnitude, m R ∼ 18, over 60 sec (Rykoff et al. 2005).They required that a transient is detected at least twice, given a cadence of 30 minutes.This limited the search to a small area of the sky, and well within the afterglow phase.Other systems strike a different balance.For instance, Mini-MegaTORTORA (Karpov et al. 2017) has a FoV of 900 deg 2 and short time resolution.However, it is limited to very bright sources, corresponding to m V ∼ 13 over 1 sec exposures.Pi of the Sky similarly has a ∼ 400 deg 2 FoV with a sensitivity, m V ∼ 12 over 10 sec (Sokolowski et al. 2009).
As indicated, most of these searches have not been sensitive to rare and faint optical flashes, shorter than ∼ 20 minutes.The main challenge has been the design of a system that combines high sensitivity, a wide FoV, and high cadence.As a result, only a small sample of untriggered GRBs have so far been identified through their afterglow emission (Cenko et al. 2013(Cenko et al. , 2015;;Stalder et al. 2017).The number of events is expected to increase in the coming years with the advent of wide-field sky surveys.A prominent example is the Zwicky Transient Facility (ZTF), which has detected 10 afterglows to date (Ho et al. 2022).
It should be noted that continuous sky coverage is critical in order to detect the short prompt emission of GRBs.This is generally not fulfilled for existing surveys, optimised for longer, SN-like timescales.For context, the high-cadence programme of ZTF includes six 30 sec visits per night over a wide area of ∼ 2500 deg 2 ; a fast ZTF transient is considered one that fades within a few nights (Andreoni et al. 2021).Excluding lucky coincidences in FoVs, shorter timescale phenomena are nominally studied with targeted follow-up of known sources (Andreoni et al. 2020b).
It becomes apparent that new experimental techniques are required in order to significantly increase our sensitivity to short optical flashes.One such approach is to employ a large number of small telescopes.An array of this kind can effectively match or surpass the capabilities of larger instruments, but at much lower cost.This is increasingly being motivated by the growing availability of off-the-shelf components, including back-sideilluminated CMOS detectors and fast optical tube assemblies (Ofek & Ben-Ami 2020).Examples include the Ground based Wide Angle Cameras (GWAC), which is one of the ground facilities of the upcoming SVOM mission (Wei et al. 2016); the Gravitational wave Optical Transient Observatory (GOTO; Dyer et al. (2018)); the two Evryscope arrays (Law et al. 2015); the upcoming Argus array (Law et al. 2022); and the Large Array Survey Telescope (LAST; Ofek et al. (2023)).
In this work we propose a blind search for early optical flashes from GRBs with a small telescope array, using LAST as a benchmark.If dedicated to GRB science, a LAST array has the potential to observe a substantial number of GRBs during their prompt and afterglow phases.The paper is organised as follows.We begin with an overview of the LAST telescope array in Sec. 2. In Sec. 3 we present the simulation parameters of our cosmological GRB event sample.This is followed in Sec. 4 with details on the simulation of the early optical emission for each event.In Sec. 5 we discuss the backgrounds relevant for a blind optical survey on short time scales.In Sec. 6 we describe the procedure for conducting the survey, and for using it to detect GRBs.We conclude with a summary and discussion of the results in Sec. 7.

THE LAST TELESCOPE ARRAY
LAST is an array of small optical telescopes.The first node of LAST is currently being instrumented at the Weizmann Astrophysical Observatory in the south of Israel, as shown in Fig. 1, and described in Ofek et al. (2023).Additional facilities are being planned, pending funding.
A single node of LAST nominally comprises 48 telescopes, installed on 12 independent mounts, which are housed inside a rolling-roof enclosure.LAST uses Xerxes equatorial mounts.These employ a pair of direct-drive motors, which can produce torques of 60 N-m (hour angle), and 33 N-m (decl.).LAST telescopes are 27.9 cm F/2.2 Rowe-Ackermann Schmidt Astrographs (RASA) from Celestron.Each has a FoV, 3. • 3 × 2. • 2 ≈ 7.4 deg 2 , when coupled to fullframe (36 × 24 mm) detectors.The cameras are of type QHY600M, with back-illuminated thermoelectrically cooled Sony IMX-455 CMOS sensors.The image quality, including seeing effects, results in a resolution of 2. ′′ 2-2.′′ 8 for sources near the centre of the field.The typical 5σ limiting magnitude of a single telescope without any filter is m inc = 19.6 over 20 sec exposures.This bandpass resembles the Gaia G bp band (Gaia Collaboration et al. 2016), as measured by Ofek et al. (2023).
The modular nature of LAST provides flexibility for conducting wide and deep surveys.Using the so-called "wide" observing mode, each telescope points at an independent field across the sky.This provides a simultaneous ∼ 355 deg 2 FoV (0.8% of the celestial sphere) at the nominal depth of 19.6 mag.Alternatively, several or all telescopes may be pointed at the same coordinates using the "narrow" observing mode.This substantially improves the sensitivity, comparable to a 1.9 m telescope.For instance, coadding 20 of the telescopes achieves a limiting magnitude, m inc = 21 (20 sec; 7.4 deg 2 ).
While LAST mounts can slew between different sky regions, individual telescope alignments are fixed.Manual intervention is needed in order to transition elements of the array between wide and narrow modes.This involves modifying the physical placement of telescopes on their mounts, followed by a software-driven alignment and calibration procedure.It is therefore impractical to change the observing mode of a particular mount during a night of automated operations.Correspondingly, we assume in the following that half of a LAST node is prearranged with the wide observation mode, and the other half uses the narrow mode.
The LAST cameras use a rolling shutter, which enables continuous readout with negligible dead time between exposures.It takes 0.7 sec to read images into memory, and up to an additional 1.5 sec to write them to disk.While in principle, this allows one to produce images with ∼ 1 sec resolution, it is advisable to choose slightly longer exposures.The primary reason is that the transition from read-noise noise to backgrounddominated noise takes place at exposure times of ∼ 5 sec.The mounts can move very quickly.For safety reasons, slewing is currently limited to speeds of up to 12 • sec −1 .It takes up to ∼ 2 sec to slew to an adjacent FoV, stabilise, and begin tracking.
A rich scientific agenda is planned for the first LAST node, as detailed in Ben-Ami et al. (2023).The planned survey will be dedicated to searches for gravitationalwave (GW) electromagnetic counterparts; the study of planetary systems around white dwarfs; the search for near-Earth objects; SNe science; and follow-up of HE neutrinos, to name just a few cases.The nominal observation pattern will involve high-and low-cadence surveys.For illustration, the high-cadence option will include eight visits per night per pointing; each visit will comprise 20 consecutive exposures of 20 sec, which will be coadded.A small fraction of the time will be devoted to target of opportunity (ToO) observations, such as follow-up of GRB alerts.
In the following, we propose an alternative observation strategy, which is optimised for serendipitous discovery of optical GRB counterparts.This can be used part of the time and/or with a subset of telescopes from the first LAST node.The same could also be the focus of another dedicated instrument.In order to inform the design of our survey, we simulate the expected GRB event rate, as described in the following.

COSMOLOGICAL EVENT RATE
The number of long GRBs per unit time at redshift, z ∼ z + dz, with luminosity, L γ ∼ L γ + dL γ , is given by We define R LGRB as the volumetric event rate of long GRBs per unit time; the factor, (1 + z) −1 , accounts for cosmological time dilation; Φ is the luminosity function of long GRBs; and dV /dz is the comoving volume element at redshift, z.We assume a flat, ΛCDM universe, where H 0 = 67.7 km sec −1 Mpc −1 , Ω M = 0.31, and Ω Λ = 0.69 (Planck Collaboration et al. 2020).
Given the connection of long GRBs to SNe, it is generally accepted that R LGRB follows the cosmic star formation rate, R SFR , (Kistler et al. 2008) where (2) Here ρ 0 is the local GRB event rate, and given z peak = 1 (Hopkins & Beacom 2006;Kistler et al. 2008).We account for a possible evolution effect in excess of the star formation rate, with δ = 0.4 (Qin et al. 2010).Finally, Θ M is the fractional galaxy mass density as a function of metallicity, as defined in Eq. 5 of Langer & Norman (2006).
We consider here the nominal luminosity range for standard GRBs (excluding low-luminosity bursts), which is log 10 (L γ [erg sec −1 ]) ∈ [50,54].The luminosity function is normalised, such that integrating the number density over the local volume recovers the observed event rate, ρ 0 = 1.3 Gpc −3 yr −1 (Wanderman & Piran 2010).In the following, we constrain ourselves to redshifts, z < 6.This is motivated by our interest in the optical emission of GRBs, which is highly suppressed by Lyman α absorption at higher redshift (Lamb & Reichart 2000).

Luminosity calibration
The objective of this study is to understand the rate of possible GRB detections with LAST.The HE emission of events should therefore be connected to observable optical signals.In principle, one could model the early optical emission of GRBs for each and every event as a low-energy extension of the prompt phase, or as part of the afterglow (Oganesyan et al. 2019;Kopač et al. 2013).However, we are currently only interested in the average properties of the entire sample.We can therefore take a simpler, data-driven approach, as described in the following.
The relation between the optical luminosity, L opt , and the corresponding flux, F opt , is The luminosity distance at a given redshift is denoted by D L ; the k -correction, K, accounts for the shift in frequency between the observed and rest frames of reference (Hogg et al. 2002).We can derive the flux from the corresponding γ-ray luminosity as where R o/γ = L opt /L γ denotes the ratio of optical to γ-ray luminosities.
We assume the following model for the spectral flux density in the optical band, given frequency, ν, and time, t: Here T opt is the temporal profile; the spectral index, β 0 , is drawn from a normal distribution with parameters, 0.79 ± 0.03 (Dainotti et al. 2020).The corresponding k -correction is Our point of reference for the analysis is the study of Cenko et al. (2009), hereafter denoted by C09.C09 compiled a sample of Swift-detected early afterglows with the Palomar 60 inch robotic telescope (P60).They derived the optical luminosity in the R C band for a common rest-frame time with respect to the beginning of the burst, t = 10 3 sec.The observations could be described by a log-normal distribution with mean, log 10 (L R [erg sec −1 ]) = 46.68,and a standard deviation of 1.04 dex.In the following, we assume that such a luminosity distribution is representative at this epoch; we use it to derive the normalisation scale for Eq. 8, as discussed in Sec.6.1.It remains to define T opt , in order to extrapolate the emission to earlier times, as described next.

Temporal profiles
The phenomenology of optical GRB light curves is very rich.For instance, Panaitescu & Vestrand (2008, 2011) identify three broad classes of the early emission, which they denote as fast/slow rises; plateaus; and decays.The raising and plateauing light curves may e.g., be attributed to geometric viewing-angle effects, or to shocks generated as the ejecta are decelerated by the external medium as part of the afterglow.Such profiles generally exhibit structured features on time scales of up to 10 3 sec.At early times, they may also be directly related to the prompt activity of the central engine of the GRB.The class of decays corresponds to about 50% of events (Oates 2023).These GRBs are characterised by a simple power-law decay of the optical flux with time.They presumably include a very fast-rising emission phase, occurring before the start of observations.(For instance, such a fast rise was observed for GRB 160625B by Troja et al. (2017).) Our focus for the current study is on very early optical detection (within tens of sec), which would potentially coincide with the prompt HE emission.We therefore model the temporal profile of GRBs based exclusively on the decay class.We assume a combination of smoothly connected segments, These correspond to the following: (i) a fast-rising pulse with duration, τ 0 ; the constants, a t and b t , determine a linear increase in flux from a relative value of 10-50% with respect to the peak; (ii) a short plateau with duration, (τ 1 − τ 0 ), having constant peak flux, c t ; (iii) an initial power-law decay phase having a temporal index, α t ; the duration of this phase relates to the typical prompt duration expected for long GRBs, denoted by τ 2 ; and (iv) a long-lasting second power-law decay phase, which extends into the afterglow; this phase is characterised by a temporal index, β t ; it is smoothly connected to the early decay via the constant, d t .
We generate different realisations of temporal profiles per GRB, based on randomised values of the parameters, as listed in Table 1.In addition, we add noise on the level of a few percent to each phase of the profile.A representative sample of light curves is shown in Fig. 2. As indicated, the choice of temporal decay indices is impactful.Choosing a steep spectrum (i.e., a high value of α t ) results in significant relative enhancement of the early time flux.We correspondingly choose a range of values that limits the variance of our sample in brightness.On average, peak magnitudes are about 2 mag brighter than those at t = 10 2 sec, and about 3 mag brighter than those at 10 3 sec.

BACKGROUNDS TO A BLIND SEARCH
The main sources of background for GRB optical flares on second-time scales are (i) cosmic rays; (ii) geosynchronous and graveyard-orbit satellites; and (iii) stellar flares, mostly from M-dwarfs.
Cosmic rays lose energy when hitting a detector, which may cause a bright spot to appear in one or two  .1. Two curves are highlighted, corresponding to the minimal and maximal values of the initial temporal decay index, αt, as indicated.The vertical gray bands illustrate 10 sec exposure intervals, interleaved with 20 sec gaps.This corresponds to our initial observation pattern, as discussed in Sec.6.2.For visual clarity, the presented profiles are normalised to a common point of reference, such that δminc = 0 for t = 50 sec.The actual reference time used in this study is 10 3 sec, where the relative normalisation is determined by the optical flux, as detailed in the text.
consecutive images.In general, taking multiple exposure is an effective way to reject this background.Additionally, cosmic rays may be identified in some cases in a single image by their shape, which is sharper than that of astrophysical point sources (van Dokkum 2001).The rate of cosmic ray artefacts in a typical image is about 0.07 deg 2 sec −1 .
Satellites may also mimic transient astrophysical sources, exhibiting flashes with durations of 0.2 sec and a brightness of 9-11 mag (Nir et al. 2021).Low-Earthorbit satellites move at velocities of hundreds of arcseconds per second and would appear as streaks in an image.On the other hand, satellites at high orbits may seem motionless.They can manifest themselves as single flashes.They can also appear as repeating flashes with similar magnitude, mapping a straight line across multiple images.The rate of occurrence of such flashes, which depends on declination, is ∼ 1.5 deg −2 hr −1 for individual flares, and ∼ 0.2 deg −2 hr −1 for repeaters.
Stellar flares are triggered by magnetic reconnection in the corona (Shibata & Magara 2011).Flares in the visible band may last from minutes to hours.They are mod-elled by a blackbody spectrum, and tend to follow fastrise and exponential-decay profiles.Small flares occur much more frequently than large ones.Based on dimensional arguments and observational data, the rise-time of such flares scales with their energy as E flare ∝ t 3 rise (Aizawa et al. 2022).So-called "superflares", which include an increase in brightens larger than 3 mag, are observed several times a year by very wide-field surveys (Howard et al. 2019).
Both cosmic ray and satellite backgrounds to GRBs may effectively be identified and rejected individually, or by taking multiple short consecutive images.Stellar flares require further attention.The lion's share of events may be rejected by cross-matching their location with known stars.For instance, the Gaia catalogue of stars is complete up to at least m G ∼ 20 in noncrowded sky regions (Boubert & Everall 2020;Gaia Collaboration et al. 2023).While fainter sources may only become visible as they flare, their temporal profiles are expected to be distinct from those of GRBs.
A direct consequence of the above, is that GRBs can not confidently be identified based on a single bright flash.Rather, it is necessary to obtain fine-grained temporal light curves, as well as long-term follow-up observations.In the following, we show how an instrument such as LAST may be used to obtain these early data.

Light-curve simulation
Observationally, a wide diversity of optical to γ-ray luminosity ratios has been observed, spanning several orders of magnitude (Kopač et al. 2013).Since we do not attempt to model the spectral energy distribution for individual GRBs, the value of R o/γ is not determined from first principles.Instead, we assign a flux ratio probabilistically, under the assumption that the L opt distribution of C09 is universal.
We do not assume a specific correlation between the brightness of events in the two bands, in accordance with observations (Yost et al. 2007b).Rather, we first generate independent collections of γ-ray luminosity distributions; we apply a given value of R o/γ to each; and finally, we fit the combination of samples to the reference distribution.We found that our initial simulation slightly overestimated the rate of bright events.This is likely due to a small mismatch in the redshift distributions between our simulation and the C09 dataset.We corrected this and simulate slightly dimmer optical emission, by shifting the reference distribution by −0.5 dex.(The compatibility of the final simulated brightness distribution is verified in Fig. 6 below.)The results for the luminosity ratio are shown in Fig. 3, where the distribution peaks for values, R o/γ ∼ 10 −5 -10 −4 .
We continue and generate a uniform distribution of GRBs in a fine-grained grid in luminosity, L γ , and redshift, z.Events are weighted according to their relative number density, per Eqs.1-5.This process is repeated for different optical to γ-ray luminosity ratios; each GRB is reweighted by the probability distribution for the corresponding R o/γ .
A simulated GRB is defined by the set of redshift, luminosity, R o/γ , β 0 , and a particular realisation of T opt .We derive the corresponding flux normalisation for Eq. 8 by integrating the spectrum over the R C band.This allows us to derive the respective flux and magnitude, m inc , over the inclusive (unfiltered) bandpass of LAST.We dim the observed emission, assuming an extinction value, A V , drawn from a reference distribution (log 10 A V = −0.63 ± 0.42; Wang et al. (2013)).Compared to the prompt phase, our reference luminosity represents a relatively late epoch of 10 3 sec.We extrapolate the flux for the early emission according to T opt .

Survey cadence
The potential of a blind survey to detect the optical flares of GRBs is directly proportional to the accessible search volume, and to the sensitivity to faint signals.Different arrangements of telescopes may be used to balance between these two factors.As discussed e.g., by Nemiroff (2003), it is possible to optimise the observing pattern, based on a set of simple assumptions.For instance, these include the spectro-temporal properties of the emission; the background conditions; the limiting magnitude of telescopes; and their slewing speed.One may subsequently maximise the number of putative detections for later follow-up.
In the current study, we illustrate a survey strategy that balances between source discovery and temporal sampling of the respective light-curve.We initially scan a large area of the sky intermittently.This is done using half of a LAST array, arranged in the wide observing mode.Given the detection of candidate events, we focus the other half of the array, arranged in the narrow mode, on the relevant FoV.This increases the sensitivity while observing the rapidly decaying emission of the source.Probing the light-curve several times has the advantage of reducing the number of fake positive detections, as discussed below.
We design the observing strategy with the objective of effectively doubling the baseline sky coverage of LAST.This may be accomplished by taking advantage of the rapid slewing capabilities of the instrument, as well as the option to deploy subsets of telescopes in wide and narrow observing modes.Using a simple wide layout of telescopes, it is possible to continuously tile a region of the sky.This is illustrated in the top panel of Fig. 4. In this case, each FoV is continuously being observed using short exposures of τ obs sec.
Alternatively, it is possible to deploy telescopes with wider margins, as e.g., shown in the bottom panel of the figure.Here we illustrate the following observing pattern: (i) take a pair of exposures (2 × τ obs ) of a particular field, designated as FoV 1 ; (ii) slew to a different field, FoV 2 ; this incurs a gap in observations of τ slew sec; (iii) take a pair of exposures, pointing at FoV 2 ; (iv) slew telescopes back to their original coordinates.This pattern constitutes a single observing cycle, which is continuously repeated until a source-candidate is detected.
For the current study, we assume that the LAST array comprises 40 telescopes, 20 of which are aligned in the wide observing mode and participate in the blind search.The other set of 20 telescopes is aligned in the narrow mode.After a potential flare is identified, the subarray of narrow/convergent telescopes is repointed onto the respective FoV.This substantially increases the sensitivity to the rapidly fading emission of the putative GRB.
We choose τ obs = 5 sec and τ slew = 5 sec, which constitutes a 1:2 cadence pattern.Correspondingly, we take exposures of 10 sec during the blind search stage (coadding 2 × τ obs exposures), which are separated by 20 sec gaps.These include slewing intervals and observations of alternative fields.For example, a possible lightcurve of exposures might correspond to t ∈ [0-10, 30-40, 60-70, 70-80, 80-90, ...] sec; this assumes a transition to narrow observing at t = 60 sec.We explicitly choose a pair of 5 sec exposures, rather than a single 10 sec one, which mitigates cosmic ray and satellite backgrounds.
The dynamic observing approach increases the number of observable events, by compromising on detection of a short segment of the initial light-curve.The success of such a strategy depends on development of efficient analysis tools, which enable fast coaddition of images and identification of flares.We note that the requirement on the precision and false-positive rate of this initial filter is not stringent, given that artefacts would quickly be identified after transition to the narrow observing mode.

Flare classification
As indicated above, GRB flares would be detected based on their light-curve.A simplistic approach could be to identify events given two or more consecutive data points that pass some signal-to-noise (S/N) threshold.In practice, this strategy is suboptimal, and may result in low detection efficiency or an overabundance of spurious detections.
An alternative strategy is to devise a test statistic, which encapsulates the signal-to-noise of the entire lightcurve, and can be mapped to a p-value (significance for source detection).For this purpose, we follow the approach developed by Sadeh (2020).We construct a toy model that illustrates the methodology.Within the scope of the current study we do not attempt to simulate the background to a realistic survey.We also assume that stellar flares are identified independently via a combination of cross-matching with stellar catalogues; a dedicated event classifier; and longer-term follow-up.
We use the open-source software, tensorflow (Abadi et al. 2015), to construct a simple neural network.The network is made up of four layers as follows: (i) two consecutive layers of 64 and 32 fully-connected neurons; (ii) a softmax layer, which maps the outer dense layer to a single number within the range, [0, 1]; (iii) a probabilistic layer, representing a normal distribution, which acts on the softmax layer.The output of this layer, denoted by ζ, serves as the test statistic for our analysis.
The inputs to the network are time series data, constructed for a putative transient source position over consecutive exposures.For the wide observing-mode segment of the light-curve, the metric per time step is the S/N for aperture photometry, which is derived using the so-called "CCD equation" (Howell 1989).We assume first detection and convergence of the narrow subarray of telescopes after 30 sec.For this observation interval, the inputs to the network correspond to the integrated S/N from all telescopes.Each light-curve Schematic representation of two blind survey strategies.For visual clarity, we illustrate here a LAST array consisting of only 12 telescopes.The top panel illustrates a "simple" wide observing layout, where the different telescopes are deployed in a continuous 3 × 4 grid in azimuth and elevation.Highlighting the FoV of one of the telescopes (denoted here as "3"), the light-curve of a putative transient source is continuously sampled in steps (exposures) of duration, τ .The bottom panel illustrates a "dynamic" observing strategy, where each telescope transitions between two FoVs, denoted collectively as FoV1 and FoV2.This corresponds to an initial sparse observing pattern for each FoV.At some point in time, denoted here as 13τ , a flare candidate is detected.Following a short interval for the candidate to be identified, multiple telescopes in the narrow alignment mode converge on the relevant field.The light curve is further sampled without gaps.comprises 14 steps, representing a total of 150 sec of observations.
The training objective for the network is to perform classification between two classes for "background" and "signal".Background data correspond to random noise, based on fluctuations of the assumed sky brightness.We add to this further upward fluctuations on the level of (10 ± 3)σ, representing single-exposure artefacts.These are injected randomly at a rate of about one fluctuation per input time series.
Data comprising the signal class include simulations of GRB optical flashes.We use the complete unweighted sample, without accounting for the relative number density on z, L γ , and R o/γ .Correspondingly, the training examples are balanced with respect to flare brightness.We apply a selection cut on the signal class.The objective is to suppress faint events that can not be distin-guished from background, which can impede the training of the network.Explicitly, we impose the condition, σ After the network is trained, the correspondence between the output, ζ, and the detection significance, σ cls , is derived numerically, as discussed by Sadeh (2020).The performance of the classifier is shown in Fig. 5.We significantly detect flares and reject background, based on the brightness and the time structure of the signal.For illustration, the detection threshold is approximately characterised by flares having σ (1) peak > 8 and σ (2) peak > 7.However, background realisations having brighter fluctuations are also rejected.This is due to (2) peak > 7), signal events may be identified with high confidence.
the fact that the network is trained to identify correlated structures within the input time series.

Detection rates
The details of our simulation are summarised in Table 1.For the moment, we assume that each and every GRB actually exhibits an optical signal.In practice, this is not realistic, as a substantial fraction of events should be designated as optically "dark" GRBs (Oates 2023).We discuss this in Sec. 7.
We begin by verifying our predictions for the reference luminosity distribution of C09, as shown in Fig. 6.The expected distribution of observed magnitudes is recovered for a comparable volumetric sample (average redshift, z avg ∼ 2).For our full dataset the distribution is fainter, as it extends to higher redshift.We find the following cumulative fractions, C < m inc , at 10 3 sec: 5% < 14.5, 20% < 17, and 50% < 18.5.
Distributions of detectable flares are presented in Fig. 7.We impose a minimal selection threshold, where light curves include at least two time steps (10 sec exposures) having S/N > 5.In addition, we require a classification detection significance, σ cls > 5.For the assumed wide subarray of 20 telescopes, operating with a 1:2 cadence, the effective survey area is approximately 300 deg 2 .We further assume the availability of 6 hours of clear sky per night, corresponding to an effective survey live-time of 0.25 yr −1 (Ofek et al. 2023).Our results correspond either to a limited redshift range, for which the average is zavg ∼ 2, or to the inclusive dataset, as indicated.The limited redshift sample is comparable to the equivalent reference data, validating the luminosity calibration procedure.Events are observable up to peak magnitudes, m (1) peak ∼ 19.5, over 10 sec exposures.In total, this survey strategy allows detection of up to about 14 GRBs yr −1 during their early emission phase.Assuming an HE flux threshold, F γ > 10 −8 erg cm −2 sec −1 , a subset of 3 GRBs yr −1 is detectable.These events would also trigger γ-ray satellites observing the same field as LAST.The rest of the events are not expected to be associated with HE triggers, but might be detectable via follow-up archival search.In reality, the expected rate of detectable GRBs is actually lower than 14 GRBs yr −1 , as discussed in next section.

SUMMARY AND DISCUSSION
We suggest an observational approach for the independent discovery of long GRBs.Events are detected via their early optical signals, with the purpose of probing the prompt phase of the emission when relevant.We explore the potential of an array of small telescopes such as LAST for this purpose.Such an instrument can be used to scan a wide region of the sky, and then focus on a smaller FoV with increased sensitivity.
We find that for our chosen array configuration, one can potentially detect 14 GRBs yr −1 .Of these, 20% would also be detectable with high confidence by γray instruments.An important caveat for this result is our assumptions on the realistic fraction of optically detectable GRBs, given that some events lack optical emission.A GRB is commonly classified as optically "dark" when the ratio of optical to X-ray flux is incompatible with the standard expectations for synchrotron afterglows 2 (Jakobsson et al. 2004).
The fraction of dark GRBs is not straightforward to estimate.Several factors may play a role in masking the observed signal.These include extrinsic effects, such as Lyman α absorption at high redshift, or high host galaxy extinction.Intrinsic suppression within the source and its environment may also play an important role.The time at which the flux in the optical and X-ray bands is compared is also determinative, and can e.g., be biased by continuous or renewed activity of the central engine.
We note that, under this definition, the optical signal of a dark GRB may yet be observed; however the flux is significantly suppressed compared to other bands.To put this in context, C09 optically detected ∼ 80% of their sample of 29 GRBs, for which follow-up began within an hour of the trigger.The fraction of bursts classified as dark for the same dataset was found to be ∼ 50%.The detection fraction inferred from Fig. 7 may therefore be more realistically estimated as 7-11 GRBs yr −1 .It is reasonable to assume that the same number of events, 3 GRBs yr −1 , would have corresponding HE triggers.These would be relatively bright events, for which stronger optical components are expected (Troja et al. 2017).However, the details depend on whether the nature of a dark burst is intrinsic or extrinsic.These numbers also depend on the assumption that it is valid to model the optical flash as synchrotron emission, which may not be the case for every GRB.
The focus of this work is the prompt optical emission of GRBs, for which few data exist as reference.Our simulations are therefore based on early time afterglow data, where we extrapolate the emission from 10 3 sec back to the moment of the explosion.The temporal decay of GRB afterglow flux at late times (hours to days in this context) is very generally compatible with f ∝ t −1 (Kann et al. 2010).We purposely choose shallower profiles at earlier times for the current study, so that we do not overestimate the flux; this is also broadly compatible with available observations (e.g., Li et al. (2012); Kopač et al. (2013)).We note that it is possible that an additional component is present in some events, directly attributed to the activity of the engine.Detecting this component is in fact the main motivation for future surveys.In this context, our predictions for the brightness of the early time signal may be considered conservative.
Previous studies involving speedy GRB follow-up are mostly of limited sample-size, and are generally biased towards early-afterglows.While such observations are not necessarily our desired point of reference, it remains interesting to compare them with our predictions.We find the following cumulative fractions, C < m inc , during the prompt phase: 2% < 12, 9% < 14, 30% < 16, 50% < 17.2, and 90% < 19.These are comparable with previous findings, e.g., those of Klotz et al. (2009); Wang et al. (2013).
We also verify that our results are compatible with established limits on the rate of fast extragalactic transients.For example, ROTSE-III, found R GRB < 1.9 deg −2 yr −1 up to m R ∼ 18 (Rykoff et al. 2005), and MASTER derived a comparable limit, R GRB < 1.2 deg −2 yr −1 up to m V = 17.5 by (Lipunov et al. 2007).(See also Table 3 of Berger et al. (2013); Fig. 6 of Andreoni et al. (2020a).)Accounting for survey coverage, live-time, and a realistic fraction of optically dark events, the current study finds an intrinsic rate of R GRB ∼ 0.12 deg −2 yr −1 .This result is consistent with the previous nondetections; it illustrates that an order of magnitude improvement in efficiency is required in order to make progress in the field.This highlights the importance of conducting very wide surveys, coupled to analyses targeting short time scale transients.

Figure 1 .
Figure 1.The first node of LAST at the Weizmann Astrophysical Observatory, with the enclosure fully opened.The array here includes 32 of the planned 48 telescopes already installed.(See Ofek et al. (2023).)

Figure 2 .
Figure2.Examples of GRB temporal profiles, Topt, represented as the change in (unfiltered) LAST magnitude, δminc, as a function of time, t, with respect to the presumed beginning of observations.The different curves illustrate various realisations, sampled from the parameter space detailed in Table.1.Two curves are highlighted, corresponding to the minimal and maximal values of the initial temporal decay index, αt, as indicated.The vertical gray bands illustrate 10 sec exposure intervals, interleaved with 20 sec gaps.This corresponds to our initial observation pattern, as discussed in Sec.6.2.For visual clarity, the presented profiles are normalised to a common point of reference, such that δminc = 0 for t = 50 sec.The actual reference time used in this study is 10 3 sec, where the relative normalisation is determined by the optical flux, as detailed in the text.

Figure 3 .
Figure 3. Distribution of the derived ratio of optical to γ-ray luminosities at 10 3 sec, where PR o/γ denotes the probability density function of R o/γ .
Figure 4.Schematic representation of two blind survey strategies.For visual clarity, we illustrate here a LAST array consisting of only 12 telescopes.The top panel illustrates a "simple" wide observing layout, where the different telescopes are deployed in a continuous 3 × 4 grid in azimuth and elevation.Highlighting the FoV of one of the telescopes (denoted here as "3"), the light-curve of a putative transient source is continuously sampled in steps (exposures) of duration, τ .The bottom panel illustrates a "dynamic" observing strategy, where each telescope transitions between two FoVs, denoted collectively as FoV1 and FoV2.This corresponds to an initial sparse observing pattern for each FoV.At some point in time, denoted here as 13τ , a flare candidate is detected.Following a short interval for the candidate to be identified, multiple telescopes in the narrow alignment mode converge on the relevant field.The light curve is further sampled without gaps.
-input of the brightest 10 sec interval of the lightcurve; σ (2) peak likewise corresponds to the second-brightest interval.This selection cut is only used for the training phase of the classification pipeline.

Figure 5 .
Figure 5. Left: Distributions of the test statistic of the classification algorithm, ζ, for the signal and background classes, as indicated.The background sample, corresponding to noise-based light curves, is clearly distinguished from most of the signal sample, which corresponds to simulated flares of various brightness.The test statistic is mapped to a significance for source detection, denoted by σ cls .Right: Relation between the S/N of the brightest and second-brightest 10 sec interval of the light-curve, respectively denoted by σ (1) peak and σ (2) peak .For visual clarity, we only include light curves for which σ (1,2) peak ≤ 15 per time step.The dataset is split into categories for the signal and background samples, corresponding to light curves that pass or fail the 5σ detection threshold of the classifier.As indicated, background light curves and faint signal examples are not significantly detected.Above a certain threshold (approximately σ (1) peak > 8 and σ

Figure 6 .
Figure 6.Comparison between the simulated GRB sample and the reference distribution from C09 (Cenko et al. 2009).The dashed line represents the distribution of RCband magnitudes, mR, for our inclusive sample, indicated as "Inc.".The full lines represent the cumulative mR distributions from C09 and for the current study, denoted by Cx.Our results correspond either to a limited redshift range, for which the average is zavg ∼ 2, or to the inclusive dataset, as indicated.The limited redshift sample is comparable to the equivalent reference data, validating the luminosity calibration procedure.

Figure 7 .
Figure7.Simulated GRBs, described by two metrics, denoted by x.In total, about 24 GRBs yr −1 would occur within the FoV of the survey, 14 of which are detectable.Out of these, three events are also expected to trigger HE instruments.(This result does not account for a suppression of the optical flux for dark GRBs, which reduces the expected detectable rate from 14 to 7-11 GRBs yr −1 , as discussed in the text.)Left: Distributions, dN/dx, of the peak light-curve magnitude, m(1) peak , of LAST.The different curves represent the full simulated sample of events ("Inc."),and the significantly detected subsample ("Det.").Also shown is the respective cumulative distribution of detected events, Cx, as indicated.Right: Distribution, dN/dx, and cumulative distribution, Cx, of the peak γ-ray flux, Fγ, for detected GRBs, as indicated.The typical threshold of γ-ray satellites, Fγ ∼ 10 −8 erg cm −2 sec −1 , is highlighted by the dotted-dashed vertical line.

Table 1 .
Summary of the parameters used to simulate the blind survey.FoV cadence (wide mode) 1:2 cadence with gaps, τ obs + 2 × τ slew = 20 sec Effective live-time 0.25 yr −1 (6 hours per night) † Unlisted parameters, at; bt; ct; and dt, are derived on a case by case basis, given the luminosity normalisation of the light-curve.