# Observing FRB 121102 with VERITAS; Searching for Associated TeV Emission

, for the VERITAS Collaboration
University of California, Los Angeles
E-mail http://veritas.sao.arizona.edu

###### Abstract:

Fast radio bursts are bright, unresolved and short flashes of radio emission
originating from outside the Milky Way. The origin of these mysterious
outbursts is unknown, but their high luminosity and short duration has
prompted much speculation. The discovery that FRB 121102 repeats has enabled
multiwavelength follow up, which has identified the host galaxy. VERITAS has
observed the location of FRB 121102, including coincident observations with
Arecibo. We present the results of a search for steady very high energy
$\gamma$-ray emission and the methodology for searching for short timescale,
transient optical and very high energy $\gamma$-ray emission.

##  1 Introduction

Fast radio bursts (FRBs) are millisecond-duration burst of high dispersion-
measure (DM) radio emission. They were first discovered in 2007 in an analysis
of archival data from 2001 July 24 taken by the Parkes observatory [1].
Subsequently many more bursts have been observed and these have enabled an
understanding of their origin start to develop.

Their high DMs and uniform distribution across the sky implies that they
originated outside the Milky Way and are thus orders of magnitude brighter
than pulses from Galactic pulsars [2]. Models were developed based upon
arguments of causality which require that the emission region is sufficiently
small to produce the observed bursts. The fastest recorded bursts are less
than 1 ms and not temporally resolved, leading to emission region sizes less
than a few tens of kilometers across. The properties of the bursts are also
highly non-thermal, with brightness temperatures reaching up to about 1037 K:
in the region of temperatures measured from “nanoshots” from pulsars. They
were initially thought to be cataclysmic events; for example, the merger of
neutron stars. The discovery that FRB 121102 repeats ruled out all of these
models (or at least rules out those models for that source. No other bursts
have yet been seen to repeat, though FRB 110220 and FRB 140514 may form a pair
[3]). The only astronomical phenomena with similar timescales that repeat are
soft gamma repeaters (which have been observed to have rise times of 200-300
$\mu$s) and pulses, sub-pulses and “nanoshots” from radio pulsars, some of
which have durations $\leq$ 0.4 ns. The properties and potential origin of
FRBs is discussed in detail in [4].

##  2 FRB 121102

FRB 121102 is unique amongst FRBs in that it has been observed to repeat. This
surprising discovery was first reported in [5] and has lead to a large
observing campaign to localize the origin and characterize the properties of
the bursts. Tendulkar et al. [6] identified the host as a dwarf Spheroidal
galaxy located at (05h31’58.70” +33°08’52.5”) and at a redshift of
z=0.19273(8) (corresponding to a luminosity distance of 972 Mpc) where a
persistent radio source has been detected. The rate of bursts has been studied
by Oppermann and Pen [7]. They reported that the repetition pattern is non-
Poissonian; rather, they fit it with a Weibull distribution with a mean
repetition rate of 5.7${}^{+3.0}_{-2.0}$ per day and index, k, of
0.34${}^{+0.06}_{-0.05}$ where a k of 1 reduces the distribution to a Poisson
distribution and the observed value ($<$ 1) shows that smaller intervals
between bursts are favored. Multi-telescope campaigns in radio (e.g. [8]) and
other wavelengths including Swift, Chandra and Fermi-LAT [9] have identified
over 100 bursts and been used to place upper limits on both the burst and
steady state X-ray and high energy $\gamma$-ray fluxes.

###  2.1 Very High Energy $\gamma$-ray Emission from FRB 121102

As non-thermal emitters at very high luminosities (reaching 1039 – 1041 ergs,
FRBs could potentially power very high energy (VHE, E $>$ 100 GeV)
$\gamma$-ray emission. At a distance of z=0.19273, VHE emission from FRB
121102 will be attenuated by interactions with the extragalactic background
light (EBL). Using the EBL model of [10] we estimate an optical depth ($\tau$)
of 0.02 at 100 GeV and 0.95 at 1 TeV. Thus we do not expect to detect a
significant flux above 1 TeV but emission in the region of 100 GeV will be
largely unaffected by the EBL. Models for VHE emission from FRBs exist.
Lyubarsky [11] generated a model based upon soft gamma ray repeaters and
predicted that millisecond VHE emission could be visible at distances up to
about 100 Mpc. In contrast, Vieyro et al. [12] proposed a model for FRB 121102
based upon an AGN and concluded that high energy emission may be detectable
for seconds to minutes after the radio burst, even for modest energy budgets.
However, the current theoretical and observational understanding of the
emission of VHE $\gamma$-rays from FRBs is very limited and VHE observations
could be useful to constrain future modeling work by helping to constrain the
total energy budget and e.

###  2.2 Optical Emission from FRB 121102

Designed to detect nanosecond pulses of Cherenkov radiation from relativistic
particle showers in the Earth’s atmosphere, imaging atmospheric Cherenkov
telescopes (IACTs) are, by design, very efficient detectors of fast optical
transients. They have previously been used to conduct optical SETI searches
[13] and to study micro-meteorites [14]. Lyutikov and Lorimer [15] predict
that, assuming the same radio efficiency as optical efficiency, FRBs will
produce millisecond flashes of magnitude, m, given by

$m=-2.5log_{10}\left(\frac{F}{3631\mathrm{Jy}}\right)$ (1)

The brightest peak flux (F) from FRB 121102 reported in [8] is 3.3 Jy, which
equates to a visual magnitude of 7.6. They also comment that the radio
emission is typically a small fraction of the total energy emitted at other
wavelengths, it therefore not unreasonable to assume that the optical emission
could be up to 100 times brighter than this, reaching a visual magnitude of
about 2.6.

A search can be conducted using the same method as outlined in [13]. In short,
the search technique looks for images which:

  1. 1.

Appear at the source location in all four telescope cameras.

  2. 2.

Have the same intensity in each telescope.

  3. 3.

Are point-like.

These criteria are sufficient to remove almost all of the background events
from the analysis since cosmic ray showers produce the majority of their light
below an altitude of 20 km. Given that the telescopes are separated by about
100 m this means that the recorded images show significant parallactic
displacement ($>$0.3°). In addition, cosmic (and $\gamma$) ray showers induce
Cherenkov light over a significant vertical distance (km’s). Therefore, again
due to the separation of the telescopes, all but (at most) one of the observed
images will be elongated.

The temporal characteristics of the light pulse also play an important role in
determining the trigger efficiency. The fastest bursts recorded thus far are
$\lesssim 1$ ms in duration, though this is faster than the radio receivers
temporal resolution so they may be shorter but, given that the majority of
burst have widths of a few ms we would not expect them to have durations
significantly less than this. The VERITAS PMT signal path is AC-coupled in the
telescope camera prior to pre-amplification, with a lower cutoff frequency of
approximately 100 kHz. This would prevent a pulse of the expected FRB duration
from triggering the array and thus prevent VERITAS from detecting such a
pulse.

There is a caveat to this, in that a steady optical source such as a bright
star in the field of view will generate high frequency Poisson noise
fluctuations in the PMT signals, increasing the probability of accidentally
crossing the discriminator thresholds. In [13] they estimated that the number
of photoelectrons produced by a B-band 6.4 mag star in the 12 ns readout
window in a VERITAS pixel is 18.8. To trigger an individual pixel requires a
pulse 4 – 5 photoelectrons [16]. With visual magnitudes potentially reaching
up to 2.9, FRBs would produce around 140 photoelectrons within 3 ns, this is
likely to be sufficient for the Poisson fluctuations to produce a trigger.

It is noted that an exact estimate of the sensitivity of the search would
prove very difficult since the minimum detectable optical pulse intensity
depends strongly upon the emission wavelength, and the duration and temporal
profile of the pulse. However, a detection would provide the first evidence of
optical bursts associated with FRBs.

##  3 VERITAS Observations

VERITAS is an array of four IACTs located at the Fred Lawrence Whipple
Observatory (FLWO) in southern Arizona (31° 40’N, 110° 57’W, 1.3 km
a.s.l.)[17]. Designed to detect the Cherenkov emission from extensive air
showers produced by cosmic and $\gamma$-rays, each telescope has a mirror area
of 110 m2 and is equipped with a 499-pixel camera of 3.5° diameter field of
view with an angular resolution of 0.1° at 1 TeV. The system, completed in
2007, is run in a coincident mode requiring at least two of the four
telescopes to trigger in each event. This design enables the observations of
astrophysical objects in the energy range from 85 GeV to $>$ 30 TeV with an
effective area $>$ 105 m2. The observations were conducted wobble mode where
the target is offset 0.5° from the center of the field-of-view to allow for
simultaneous background estimation. The large effective area (over 10,000 m2
at 1 TeV, cf. Fermi-LAT which reaches just less than 1 m2 at 1 GeV [18]) and
low dead time ($<$ 10%, about 20 $\mu$s per event) combined with a low
background rate (around 1 per minute within 0.1° of a given location after
gamma/hadron selection cuts) makes VERITAS an ideal candidate to search for
fast, transient signals such as those that could be emitted from FRB 121102.

Initial observations were conducted in 2016 March, totaling 3.35 hours of live
time, without contemporaneous radio coverage. Additional observations were
conducted in 2016 Fall and 2017 Winter which totaled 6.48 hours of live time
and were conducted coincident with Arecibo observations. In total, 10.83 hours
of live time was taken on the source.

##  4 Continuous VHE Emission

The standard VERITAS analysis techniques as described in [19] were used to
search for continuous TeV emission with the gamma/hadron selection cuts tuned
to search for soft spectrum sources such as we would expect from FRB 121102
after EBL attenuation.

No VHE emission was detected from the position of FRB 121102 or the
surrounding area. At the location of FRB 121102 the significance was
-1.51$\sigma$. A significance sky maps of the region is shown in fig. 1, along
with a histogram of the significances, which is well fit by a normal
distribution. The mean significance was -0.086$\pm$0.006 and the standard
distribution was 1.106$\pm$0.006. This shows that no sources were detected in
the field of view.

Figure 1:  Left: Map of the significances for the region surrounding FRB
121102. The location of FRB121102 is shown by the cyan diamond, the point
spread function is shown by the black circle in the upper left corner Right: A
histogram of the significances for the entire map. Overlaid is a normal
distribution (red line).

Given the non-detection of continuous VHE emission from FRB 121102, an upper
limit on the flux was calculated using the method of Rolke [20] at the 95%
level and using the bounded solution. Differential flux upper limits were
calculated using spectral indices of -2 and -4 at 5.2$\times 10^{-12}$ and
4.0$\times 10^{-11}$ cm-2 s-1 TeV-1 at their respective energy thresholds of
0.2 and 0.15 TeV. Here, the energy threshold is defined as the peak of the
efficiency distribution: the effective area multiplied by a power law spectrum
of -2 and -4 respectively.

Searches were also conducted on a run-by-run basis to search for emission on
shorter time scales, no evidence of emission was found with a maximum
significance in a single run of 2.1$\sigma$, before accounting for the
statistical trials involved in searching many runs. Differential upper limits
were also calculated and are given in table 1.

Table 1: VERITAS run by run results, showing, for each observing run, the start and end time, the live time (in minutes, after removal of periods of bad weather and accounting for deadtime), the significance of that runs observations, and, for two different spectral indices, the energy threshold (EThresh) in TeV and the differential upper limit at the energy threshold (in cm-2 s-1 TeV-1). MJD Start | MJD End | Live | Sig. | Index = -2 | Index = -4
---|---|---|---|---|---
Time | EThresh | DUL | EThresh | DUL
57451.104884 | 57451.125718 | 23.78 | 0.31 | 0.14 | 1.11e-10 | 0.12 | 6.31e-10
57451.1264 | 57451.147234 | 20.06 | -2.99 | 0.14 | 3.22e-11 | 0.13 | 1.58e-10
57456.13441 | 57456.155243 | 25.89 | 0.57 | 0.15 | 8.96e-11 | 0.14 | 3.72e-10
57456.156493 | 57456.177326 | 26.25 | 0.16 | 0.18 | 5.18e-11 | 0.17 | 2.26e-10
57457.166262 | 57457.187106 | 25.89 | -0.25 | 0.18 | 4.26e-11 | 0.17 | 2.04e-10
57457.18787 | 57457.208704 | 26.28 | -0.09 | 0.26 | 2.32e-11 | 0.24 | 9.07e-11
57458.184028 | 57458.204861 | 26.39 | -1.17 | 0.24 | 1.58e-11 | 0.22 | 6.92e-11
57459.17772 | 57459.198565 | 26.35 | 1.39 | 0.24 | 4.85e-11 | 0.22 | 2.05e-10
57686.280347 | 57686.301192 | 14.08 | 0.1 | 0.38 | 8.77e-12 | 0.35 | 4.29e-11
57686.301539 | 57686.322373 | 26.44 | 0.76 | 0.29 | 2.64e-11 | 0.26 | 1.21e-10
57686.322882 | 57686.343715 | 25.93 | -0.31 | 0.24 | 2.27e-11 | 0.22 | 9.59e-11
57686.344421 | 57686.365266 | 26.36 | -1.26 | 0.2 | 1.34e-11 | 0.18 | 5.34e-11
57717.237118 | 57717.257951 | 27.05 | -0.5 | 0.22 | 3.2e-11 | 0.2 | 1.52e-10
57717.258368 | 57717.279201 | 26.83 | 0.94 | 0.18 | 9.36e-11 | 0.17 | 4.84e-10
57727.210486 | 57727.231319 | 25.61 | -1.48 | 0.22 | 1.9e-11 | 0.2 | 8.1e-11
57727.231956 | 57727.252789 | 25.84 | -0.44 | 0.18 | 4.53e-11 | 0.17 | 1.89e-10
57731.16684 | 57731.187685 | 25.79 | -0.26 | 0.32 | 9.35e-12 | 0.29 | 3.98e-11
57731.188229 | 57731.209062 | 27.38 | 1.4 | 0.24 | 2.48e-11 | 0.2 | 1.44e-10
57731.210127 | 57731.230961 | 27.53 | 0.46 | 0.18 | 2.75e-11 | 0.17 | 1.32e-10
57731.231528 | 57731.241944 | 13.99 | 2.07 | 0.17 | 8.43e-11 | 0.15 | 3.78e-10
57746.163796 | 57746.184641 | 26.94 | -0.7 | 0.22 | 3.15e-11 | 0.18 | 1.96e-10
57746.185081 | 57746.19059 | 6.86 | 1.08 | 0.18 | 2.37e-10 | 0.17 | 1.24e-09
57746.197743 | 57746.208218 | 10.26 | -0.91 | 0.15 | 8.16e-11 | 0.14 | 3.54e-10
57772.085938 | 57772.106771 | 25.67 | -0.14 | 0.22 | 3.51e-11 | 0.2 | 1.54e-10
57772.107315 | 57772.128148 | 25.72 | 0.0 | 0.18 | 5.52e-11 | 0.17 | 2.5e-10

A $\sim$0.2 mJy persistent radio source [21] has been detected that is both
compact ($<$ 0.7 pc) and coincident with FRB 121102 [22]. At this distance,
all of the known VHE $\gamma$-ray galactic sources would not be visible, being
several orders of magnitude below the sensitivity of VERITAS. Taking the Crab
Nebula as a model (chosen due to its potential similarity to the host of the
the FRB source) and scaling the VHE $\gamma$-ray luminosity by the ratio of
its radio luminosity and the radio luminosity of the persistent counterpart to
FRB 121102 (4$\times 10^{5}$ [21]) would give a VHE luminosity of 7$\times
10^{35}$ s-1 TeV-1, or an observed flux of 3$\times 10^{-15}$cm-2 s-1 TeV-1 at
0.2 TeV. This is approximately three orders of magnitude lower than the
current upper limit (ignoring any attenuation in the VHE $\gamma$-ray flux by
the EBL).

##  5 Pulsed VHE Emission

Since FRBs, by their very nature, are not continuous emitters, an analysis
looking for bursts of VHE emission is highly desirable. This can be conducted
in one of two ways:

Blind:

A search is conducted without any knowledge of whether a burst occurred. This
technique requires searching for an excess in emission within a given time
window above the expected background rate. The background rate is typically
estimated from the data by scrambling either the positions or the times of the
observed events and performing the same search, this can be repeated many
times to reduce the statistical errors. The proposed methodology is based upon
the primordial black hole search conducted by Archambault [23] with the
additional constraint that bursts must be originating from the direction of
FRB 121102.

Targeted:

Using knowledge of the occurrence of burst from simultaneous radio
observations, a search is conducted around the time of a burst, looking for an
excess in emission. A similar technique is employed to estimate the background
as for the blind analysis, however, since the time of the burst is known, the
number of statistical trials is dramatically reduced.

Given that bursts have not always been observed by all radio telescopes
conducting concurrent observations, it is worth conducting a blind search in
addition to the targeted search. However, to prevent bias, the targeted search
is conducted first. Since observations have been conducted both with and
without simultaneous radio coverage a decision has been made to not conduct
the blind search until the contemporaneous data has been analyzed. If bursts
are detected in the targeted search then that knowledge can be used to reduce
the number of different statistical tests which will be conducted (for
example, the number different window sizes), increasing the statistical
significance of any signal which is observed. The results of the simultaneous
Arecibo observations are not currently publicly available, thus the burst
search has not yet been conducted.

##  6 Pulsed Optical Emission

As with the VHE burst search, an optical pulse search can be either conducted
blind or targeted. A blind search will look for any optical flashes that occur
anywhere within the duration of the observations. In contrast, a targeted
search will look just in a small time window around any observed burst. In
order to not bias the results, as for the VHE burst search, the targeted
optical burst search will be conducted prior to the blind burst search and
after the Arecibo observations have been published.

##  7 Conclusions

10.83 hours (live time) of VERITAS observations have been conducted on FRB
121102. A steady state analysis of the region did not detect any evidence of
VHE $\gamma$-ray emission and upper limits on the VHE flux of 5.2$\times
10^{-12}$ and 4.0$\times 10^{-11}$ cm-2 s-1 TeV-1 at their energy thresholds
0.2 and 0.15 TeV were measured for spectral indices -2 and -4 respectively.
This is approximately three orders of magnitude above the VHE flux that would
be expected assuming a Crab nebula like source scaled to match the luminosity
of the persistent radio source located in the host galaxy. Following the
publication of the Arecibo observations we will conduct targeted and blind
burst searches on the VERITAS data, searching for both VHE and optical
emission.

##  8 Acknowledgements

This research is supported by grants from the U.S. Department of Energy Office
of Science, the U.S. National Science Foundation and the Smithsonian
Institution, and by NSERC in Canada. We acknowledge the excellent work of the
technical support staff at the Fred Lawrence Whipple Observatory and at the
collaborating institutions in the construction and operation of the
instrument. The VERITAS Collaboration is grateful to Trevor Weekes for his
seminal contributions and leadership in the field of VHE gamma-ray
astrophysics, which made this study possible.

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