# Prompt Detection of Fast Optical Bursts with the Vera C. Rubin Observatory

Guillem Megias Homar Department of Aeronautics and Astronautics, Stanford
University, Stanford, CA 94305, USA  Kavli Institute for Particle Astrophysics
and Cosmology, Stanford University, Stanford, CA 94309, USA  SLAC National
Accelerator Laboratory, Menlo Park, CA 94025, USA  Vera C. Rubin Observatory,
Colina El Pino Casilla 603, La Serena, Chile  Joshua M. Meyers Vera C. Rubin
Observatory, Colina El Pino Casilla 603, La Serena, Chile  Lawrence Livermore
National Laboratory, Livermore, CA 94550, USA  Steven M. Kahn Kavli Institute
for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA
94309, USA  SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
Vera C. Rubin Observatory, Colina El Pino Casilla 603, La Serena, Chile
Departments of Physics and Astronomy, University of California, Berkeley,
Berkeley, CA 94720, USA Guillem Megias Homar<EMAIL_ADDRESS>
(Received March 5th, 2023; Revised April 3rd, 2023; Accepted April 6th, 2023)

###### Abstract

The transient optical sky has remained largely unexplored on very short
timescales. While there have been some experiments searching for optical
transients from minutes to years, none have had the capability to distinguish
millisecond Fast Optical Bursts (FOB). Such very fast transients could be the
optical counterparts of Fast Radio Bursts (FRB), the prompt emission from
$\gamma$‐Ray Bursts (GRB), or other previously unknown phenomena. Here, we
investigate a novel approach to the serendipitous detection of FOBs, which
relies on searching for anomalous spatial images. In particular, due to their
short duration, the seeing distorted images of FOBs should look
characteristically different than those of steady sources in a standard
optical exposure of finite duration. We apply this idea to simulated
observations with the Vera C. Rubin Observatory, produced by tracing
individual photons through a turbulent atmosphere, and down through the optics
and camera of the Rubin telescope. We compare these simulated images to
steady-source star simulations in 15 s integrations, the nominal Rubin
exposure time. We report the classification accuracy results of a Neural
Network classifier for distinguishing FOBs from steady sources. From this
classifier, we derive constraints in duration-intensity parameter space for
unambiguously identifying FOBs in Rubin observations. We conclude with
estimates of the total number of detections of FOB counterparts to FRBs
expected during the 10-year Rubin Legacy Survey of Space and Time (LSST).

Optical bursts (1164) — Burst astrophysics (187) — Radio transient sources
(2008) — High energy astrophysics (739)

††journal: Astrophysical Journal††software: Batoid (Meyers et al., 2019),
Galsim (Rowe et al., 2015), IPython (Pérez & Granger, 2007) Matplotlib
(Hunter, 2007), NumPy (Harris et al., 2020), PyTorch (Paszke et al., 2019)

##  1 Introduction

Time-domain astronomy has attracted enormous interest in the community in
recent years, as new facilities come on line that dramatically improve our
capability for transient detection and source characterization. While much of
the attention has been focused on traditional classes of variable stars and
supernova explosions, the study of very fast transients has also gained
substantial momentum. That field began with the serendipitous detection of the
first $\gamma$-Ray Bursts (GRBs) in 1967 (Klebesadel et al., 1973) and the
subsequent searches for counterparts at optical, X-ray, infrared and radio
wavelengths (Paczynski & Rhoads, 1993; Panaitescu et al., 1998; Gehrels et
al., 2004). More recently, the discovery of the first Fast Radio Burst (FRB)
in 2007 (Lorimer et al., 2007), with a duration less than 5 milliseconds, has
led to a new era in fast transient astronomy.

Despite the renewed interest, however instrumental limitations make the search
for Fast Optical Bursts (FOBs) very challenging, and, as a consequence, the
transient optical sky on very short timescales has remained largely
unexplored. There have been many searches for optical transients with
durations down to minute timescales: the Palomar Transient Factory on the 48
inch Samuel Oschin telescope at Palomar Observatory (Law et al., 2009), the
ATLAS optical domain survey that reported the first discovery of a Fast Blue
Optical Transient (FBOT) (Prentice et al., 2018), the Zwicky Transient
Facility that reported a larger sample of FBOTs (Ho et al., 2021) and has been
used for the search of dirty fireballs (Ho et al., 2022), the Dark Energy
Survey (Andreoni et al., 2019), but none of these had the capability to
recognize millisecond optical bursts. The very short timescales involved, and
the presumed rarity of such events preclude most conventional approaches to
such studies. Currently, only the Tomo-e Gozen wide-field high-speed camera on
the Kiso 1.0-m Schmidt telescope capable of 0.2 ms accuracy (Sako et al.,
2018) would be able to directly detect such events using millisecond-long
exposures.

FOBs could have multiple origins: optical counterparts of FRBs, prompt
emission from fast GRBs or other previously unknown phenomena. The highly
energetic emission mechanisms that give rise to FRBs (Lyutikov, 2017; Petroff
et al., 2019; Zhang, 2020) should also produce both prompt and afterglow
emission in the optical band (Yang et al., 2019). For GRBs, afterglows have
been widely observed and studied for many years (Sari & Piran, 1999; Akerlof
et al., 2000), but the detection of prompt emission is far less common. In
both cases, the discovery of FOB counterparts would further elucidate our
understanding of the progenitor and environment of such exotic events.

The conjunction of the CHIME/FRB Collaboration with other experiments has now
yielded a substantial increase in FRB observational data (The CHIME/FRB
Collaboration et al., 2021; Caleb et al., 2017; Bhandari et al., 2018).
However, the extremely short duration precludes multi-wavelength followup via
traditional target-of-opportunity campaigns. The exception involves the
relatively small fraction of FRBs that are known to be repeating (Caleb et
al., 2018), for which simultaneous observing campaigns in multiple bands can
be coordinated (Hardy et al., 2017; Eftekhari et al., 2018). To date these
have resulted in only a single detection of an optical transient spatially
coincident with the repeating FRB180916B, which had an association probability
of 0.04% (Li et al., 2022). As for GRBs, the majority of searches for FRB
counterparts have focused on afterglow multi-wavelength counterparts (Petroff
et al., 2014; Núñez et al., 2021; Marnoch et al., 2020) as opposed to prompt
emission.

The principal obstacle to the search for FOBs lies in the scarcity of such
events. For uniformly distributed sources, the detection rate expected for
bursts of a given fluence is proportional to the volume of space that can be
surveyed to that fluence level at any given time. That volume is in turn
proportional to the product of the cube of the diameter of the primary mirror
and the field of view of the camera. The upcoming Vera C. Rubin Observatory,
with its 8.4 m Simonyi Survey Telescope and $9.6\ \mathrm{deg^{2}}$ LSST
Camera will provide a factor of nearly 20 improvement in this parameter over
all existing and planned facilities operating in the optical band. As such,
the Rubin Observatory offers the possibility of a dramatic advance in our
ability to search for FOBs, if very short duration events can be uniquely
identified in the images.

Here, we investigate a novel approach to the serendipitous detection of FOBs
through the fact that their seeing distorted images should look
characteristically different than those of steady sources in a standard
optical exposure of finite duration. In particular, for a steady source, the
Point Spread Function (PSF) due to seeing involves an average over the
distortions due to atmospheric turbulent structures that transit over the
aperture while the image is being collected. In contrast, a fast optical flash
of very short duration will exhibit distortions due to a much more limited
patch of sky given by the projection of the primary aperture on the turbulent
layers. As such, the PSF will exhibit structure at higher spatial frequencies.

Figure 1: Set of simulated images. On the left, a 15 ms simulated FOB, on the
middle a 150 ms FOB, and on the right a 15 s steady source. Top row shows the
actual LSST Camera pixelization. Bottom row shows images with higher
granularity.

In this work, we apply this idea to simulated observations from the Rubin
Observatory. We simulate FOB observations by tracing photons both through an
atmospheric model and through an optical model of the Rubin Observatory
telescope. We compare these simulations to point-source star simulations of 15
s duration, the nominal Rubin exposure time. We then introduce a Neural
Network classifier that discriminates between PSFs of optical flashes and
steady sources. We report its performance and derive constraints in the
duration-intensity parameter space for identifying FOBs in Rubin observations.
Finally, we present an estimate of the total number of Rubin Observatory
detections of FOB counterparts to FRBs expected during the 10-year Large
Survey of Space and Time (LSST). For that estimate, we assume two different
optical-to-radio fluence ratios. Our results reinforce the importance of
building the scientific capability to identify FOBs into Rubin Observatory
pipelines.

##  2 Methods

###  2.1 Simulation Model

To generate images of fast optical flashes of different durations and
intensities, we performed sequential photon by photon tracing that interfaced
several different models. In particular, we used the Ellerbroek model
(Ellerbroek & Cochran, 2002) to simulate the atmospheric structure by a series
of frozen phase screens drifted by wind velocity vectors, with each screen
covering the turbulence between two altitudes. We then generated the
atmospheric PSF by convolving the PSF of the different screens averaged during
the FOB duration. Because of the short burst duration, we cannot use the two-
bounce raytrace approximation introduced by (Peterson et al., 2015), since
that relies on temporal averaging. Instead, we compute the full Fourier
transform diffraction integral over the phase screen. For each burst we then
convolve a square-shaped burst profile with the time-dependent atmospheric
PSF, thus obtaining the FOB effective PSF. We sample this PSF with a discrete
number of individual photons consistent with the burst fluence that we are
modeling. The atmospheric seeing used in these simulations was of 0.67 arcsec
of Full-Width Half Maximum (FWHM) and Fried parameter $r_{0}=0.11$ m. In
general, larger values for seeing would reinforce the differences between FOBs
and steady sources. For convenience, the wavelength of the photons is set to
754.06 nm, which corresponds to the central wavelength of the Rubin
Observatory i-band, but the wavelength dependence is relatively weak for all
of the six bands. We used the galsim python package (Rowe et al., 2015) for
this PSF generation part of the simulation.

The photons are then traced through the optical model of the Rubin Observatory
available in the batoid python package (Meyers et al., 2019). The photons are
finally traced into the LSST Camera sensor accumulating them into the CCD
pixels using the galsim python package. This part took into account different
camera physical effects and systematic errors. In particular, we included the
Tree-Ring effect (Park et al., 2020) and Brighter-Fatter effect (Lage et al.,
2017). Once the images were obtained, the background level noise was added
based on anticipated sky levels for the i-band of the Rubin Observatory
(Ivezic et al., 2010). All of the simulated images are 20 px x 20 px in size.

###  2.2 Datasets

Different datasets of FOB images were generated along with simulated 15 s
steady-source observations. More precisely, we generated 2000 observation
images for FOBs with durations from 5 ms to 1000 ms and fluences from $8.80\
\mathrm{Jy\ ms}$ down to $0.23\ \mathrm{Jy\ ms}$. Additionally, we introduced
a dataset with 3000 cosmic ray images taken from real Rubin Observatory
Commissioning Camera dark flats that were generated explicitly for this study.

###  2.3 Neural Network classifier

To discriminate between FOBs and steady sources, we trained a deep
convolutional Neural Network (NN) on a training dataset of 4000 images, for
ten different reference fluence values. We used labeled subsets of 2000 images
of 15 s steady sources and 2000 images of 15 ms FOBs. All the images were
normalized prior to their use, to base our classification exclusively on the
PSF shape, regardless of its intensity. We used transfer learning and based
our NN structure on the VGG-16 deep neural network (Simonyan & Zisserman,
2014). We trained the classification network for 20 epochs over 10,000
training samples in batches of 256 for each of the fluence reference levels.
Throughout the training, we evaluated the network on the training set to track
its performance. After training was complete, we confirmed that the network’s
score on the testing set was close to that obtained on the training set. We
used the Pytorch Python package to implement and train the networks (Paszke et
al., 2019).

The performance of our NN classifier was then measured by evaluating our
classifier on simulated FOB images of different durations and steady-sources
images at the same 15 s fluence. Since fluence is directly measured in the
images, we apply the trained classifier for the specific measured fluence
level. We define two different metrics to characterize the classifier
performance: completeness and purity. The completeness is the percentage of
input FOBs that are correctly classified by the NN. The purity is the
percentage of events classified as FOBs that actually are FOBs.

##  3 Results

###  3.1 Simulation Model

As expected, our simulated images show a distinct difference in the PSF
structure between short duration FOBs and 15 s steady sources, where 15 s is
the Rubin Observatory nominal exposure. In Figure 1, we present a sample of
these images, both at the actual LSST Camera pixelization, and at higher
granularity, in order to better illustrate the PSF shape differences. It is
apparent from the images that the short duration events exhibit a higher
degree of speckling. Even with the loss of information that occurs when the
photons are accumulated into pixels, the characteristic differences in PSF
structure for the short bursts are preserved. This establishes the feasibility
of building a PSF classifier that has the potential to distinguish FOBs. The
simulated images in Figure 1 correspond to $8.80\ \mathrm{Jy\ ms}$ events.

The Brighter-Fatter effect is a non-linear effect in CCDs in which a brighter
point source produces a wider image, due to the mutual repulsion of
photoelectrons as they begin to fill the pixel potential wells. It can play an
important role for higher fluence events. Figure 2 presents a comparison
between a simulated image from a $15\ \mathrm{ms}$ FOB in the LSST sensor
including and excluding the Brighter-Fatter effect and related tree ring
effects. The comparison is made for sources of $8.80\ \mathrm{Jy\ ms}$, the
highest fluence that we have considered. As can be seen, some of the high-
frequency structure in the PSF is made more diffuse by the Brighter-Fatter
effect, but not enough to prevent the discrimination between FOBs and steady
sources.

Figure 2: Comparison between a simulated image from a $15\ \mathrm{ms}$ FOB in
the LSST sensor including and excluding the Brighter-Fatter and tree rings
effects.

###  3.2 Neural Network classifier

In Figure 3 we plot the completeness and purity of our NN classifier as a
function of the duration and intensity of the burst. Very high completeness is
obtained for short durations (from 5 ms to 30 ms) and a broad range of fluence
levels (from $8.80\ \mathrm{Jy\ ms}$ to $3\ \mathrm{Jy\ ms}$). We also obtain
relatively high purity $>80\%$ in this range. That provides confidence that
the approach we have described is capable of detecting and discriminating FOBs
in Rubin images with reasonable reliability.

Figure 3: Completeness and purity of the NN classifier for datasets of FOBs
with different durations and different fluences.

For longer burst durations, the completeness decreases as the PSF starts to
more closely resemble that of a steady source. We also find low completeness
at low fluence, $<1.17\ \mathrm{Jy\ ms}$. In this range, photon counting
statistic fluctuations mask the high frequency structure in the PSF for both
FOBs and steady sources, so that it becomes impossible to tell them apart.
However the purity remains high, given the small fraction of images which are
still classified as FOBs. In fact, slight tuning of the NN at low fluence
leads the classifier to exhibit either high completeness and low purity, or,
conversely, low completeness and high purity. The percentage of false
positives remains constant around 10% until it climbs for lower fluences, at
which our discriminating power decreases.

We also trained a classifier to recognize cosmic rays and to discriminate them
from both FOBs and steady sources. The purity of this classifier in
discriminating cosmic rays is 95%. Therefore, we do not expect the presence of
cosmic rays in real Rubin images to preclude FOB detection.

##  4 Discussion

If confirmed, the existence of Fast Optical Bursts would open a new channel of
investigation in transient astronomy, and would help to elucidate the physical
mechanisms that underlie such exotic phenomena. Our results show that if such
bursts exist, we should be capable of detecting them. Indeed, the simulation
results shown in Figure 1 highlight the structural differences in the PSFs
between FOBs and steady sources. We have devised a simple NN-based classifier
that can detect and discriminate FOBs of very short duration. The strength of
the deep convolutional NN classifier resides in the fact that it learns to
differentiate between subtle differences in PSFs that cannot easily be
characterized through simple statistical metrics. Nonetheless, a look into the
power spectral density in the two directions of the image sheds light on these
differences. In Figure 4 we present the power spectral density in the
$x$-direction for dataset FOB images of 15 ms and 15 s, we include both the
highest considered fluence ($8.8\ \mathrm{Jy\ ms}$) and the lowest ($1.1\
\mathrm{Jy\ ms}$). While the higher fluence images show a characteristic
difference at higher frequencies, the lower fluence power spectra are noise-
dominated at those frequencies, making the difference indiscernible.

Figure 4: Comparison of the mean and variance of the power spectral density in
the $x$-axis for 15 s and 15 ms FOB simulated images for the $8.8\ \mathrm{Jy\
ms}$ and $1.1\ \mathrm{Jy\ ms}$ fluence level. The power spectral density of
the noise is shown in pale purple.

Despite the $>80\%$ completeness for short burst durations, there is a
noticeable decrease in completeness for durations of 30 ms and longer. That is
a natural consequence of the averaging over turbulent structures in the
atmosphere with time. By 40 ms, the FOB images begin to closely resemble those
of steady sources. Further improvements in completeness might be achievable by
explicitly training the NN on samples of longer duration FOBs. In the current
study, we trained the NN only with 15 ms FOBs.

The nominal Rubin operations plan involves two sequential exposures, each of
15 s duration, for each ”visit” to a given field in the sky. Alternatively, a
single 30 s exposure could be performed, which would slightly improve the
observing efficiency of the survey, since it would avoid the second 4 s
readout of the CCDs. While the longer single exposure would marginally
increase the distinction between FOB and steady-source PSFs, the two-exposure
mode is preferred for FOB detection, since it provides an easy way to develop
a candidate set of short duration events through comparison of the two images.
Given such a candidate set for each visit, it would be straightforward to
analyze those particular images for evidence of very short-duration burst
structure. Image subtraction of the two images would also provide a means of
eliminating source crowding effects from galaxies and other steady sources in
the field. We strongly advocate that Rubin stay with its nominal operations
plan to retain sensitivity for fast transient astronomy.

While the possibility of entirely new phenomena that give rise to FOBs is
especially exciting, it is of interest to estimate how many such events might
be detected with Rubin as prompt counterparts to FRBs. The CHIME experiment
measures an FRB all-sky rate at $600\ \mathrm{MHz}$ of $525\pm 30\
\mathrm{sky^{-1}\ day^{-1}}$, to a fluence limit of $5\ \mathrm{Jy\ ms}$. We
can extend this to calculate the FRB sky rates at different fluence limits
using the fluence index $\alpha=-1.40\pm 0.11$ (The CHIME/FRB Collaboration et
al., 2023; The CHIME/FRB Collaboration et al., 2021). We then assume two
possible representative optical-to-radio fluence ratios not motivated by any
particular theoretical model ($\eta=0.1$ and $\eta=0.5$) to compute the
estimated total number of FOBs that could be detected over the 10-year LSST
Survey. From our simulations, we adopt the completeness factor associated with
each fluence threshold considered, for the discrimination of FOBs in the Rubin
images. The results of these calculations are shown in Table 1.

Note that the number of expected events is not huge, but is still large enough
to yield a statistically meaningful sample. The results do indicate, however,
that a study like this is only feasible with Rubin given its factor 20
advantage over all other facilities. It is therefore crucial for a classifier
like the one we have developed to be incorporated into the Rubin science
pipeline in order to enable a meaningful search for millisecond FOBs.

Table 1:  Estimated total FOB detections during the Large Survey of Space and Time (LSST) extrapolated from the FRB rates at 600 MHz obtained by CHIME. Fluence | Completeness | FRB rate | $\eta$ | Survey FOBs
---|---|---|---|---
(Jy ms) |  | (events/sky/day) |  | (events)
$\geq$ 2 | 68.05 % | 1893 $\pm$ 108 | 0.1 | 26.03
|  |  | 0.5 | 130.15
$\geq$ 4 | 70.8 % | 717 $\pm$ 41 | 0.1 | 10.26
|  |  | 0.5 | 51.31
$\geq$ 6 | 74.4 % | 406 $\pm$ 23 | 0.1 | 6.11
|  |  | 0.5 | 30.56
$\geq$ 8 | 80.9 % | 271 $\pm$ 15 | 0.1 | 4.44
|  |  | 0.5 | 22.2

##  5 Conclusions and Future Work

We have introduced a novel approach to detecting Fast Optical Bursts. The
existence of FOBs would bring invaluable new information to the study of fast
transient events, either FRBs, GRBs or other unknown phenomena. We simulated
the PSFs of different FOBs using a Rubin Observatory simulation model and
reported a successful approach for discriminating them from steady sources.

In summary: (1) Our simulation model showed that PSF structures for
short‐duration FOBs are distinctively different than those of steady sources.
(2) The combination of high completeness ($\mathbf{>70\%}$) and high purity
for FOBs above 3 Jy ms and shorter than 30 ms, make the certainty of our
classification algorithm reliable. (3) The estimated FOB rates for FRB
counterparts indicate that a study like this is only possible with Rubin, not
with any of the smaller precursor surveys.

There are a variety of ways in which our work could be extended. First and
foremost, our results make a case for building the scientific capability of
detecting these bursts into the Rubin Observatory scientific pipelines. The
integration and refinement of our classifier into the Rubin pipelines, and the
introduction of FOB source injection prior to first light are the main
activities to be pursued.

This material is based upon work supported in part by the National Science
Foundation through Cooperative Agreement AST-1258333 and Cooperative Support
Agreement AST1836783 managed by the Association of Universities for Research
in Astronomy (AURA), and the Department of Energy under Contract No. DE-
AC02-76SF00515 with the SLAC National Accelerator Laboratory managed by
Stanford University. The project leading to these results also received
funding from “la Caixa” Foundation (ID 100010434), under the agreement
LCF/BQ/EU21/11890114. This research made use of Stanford University
computational resources. We thank Lynne Jones, Zeljko Ivezic and HyeYun Park
for helpful discussions. G.M. thanks the LSSTC Data Science Fellowship
Program, which is funded by LSSTC, NSF Cybertraining Grant #1829740, the
Brinson Foundation, and the Moore Foundation; his participation in the program
has benefited this work. The Vera C. Rubin 8.4m Simonyi Survey Telescope
Observatory

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