Limits on Simultaneous and Delayed Optical Emission from Well-localized Fast Radio Bursts

Fast radio bursts (FRBs) are incredibly bright, millisecond-duration pulses at GHz frequencies (e.g., Lorimer et al. 2007; see Petroff et al. 2019, 2022 for reviews). Their dispersion measures (DMs), the integrated electron column density along the line of sight, exceed the range of the Milky Way (MW) plus its halo, implying an extragalactic origin. While most FRBs appear as one-off events, a growing subset are known to repeat (e.g., Spitler et al. 2016; see CHIME/FRB Collaboration et al. 2019 and Fonseca et al. 2020 for sample studies), and it is possible that the entire population repeats on a wide range of timescales (e.g., Nicholl et al. 2017; Ravi 2019; Cui et al. 2021). To date, about 20 FRBs (both one-off and repeaters) have been precisely localized through their radio emission, providing an initial, though potentially biased, view of their host-galaxy environments (see, e.g., Chatterjee et al. 2017; Marcote et al. 2017; Tendulkar et al. 2017; see further Heintz et al. 2020; Bhandari et al. 2022), and directly confirming their extragalactic origin.

Despite the rapidly increasing sample size and the availability of some localizations and host-galaxy properties, the physical origin(s) and mechanism(s) of FRBs remain unknown, with dozens of proposed sources and emission mechanisms published to date (see, e.g., Platts et al. 2019 for a living list of theoretical FRB models). ¹⁶ Given the short duration and noncatastrophic nature of the repeating FRBs, models involving young neutron stars or black holes are particularly popular; the recent faint FRB-like detection from the Galactic magnetar SGR 1935+2154 may support such a picture (CHIME/FRB Collaboration et al. 2020a; Bochenek et al. 2020). Some of the precisely localized extragalactic FRBs (e.g., FRB 20200120E in an M81 globular cluster; Bhardwaj et al. 2021; Kirsten et al. 2022a) show no correlation with star formation, possibly indicating an origin from older neutron stars, accretion-powered binaries (e.g., Sridhar et al. 2021), or from young magnetars born from an older progenitor channel (e.g., accretion-induced collapse of white dwarfs or the merger of two neutron stars; Margalit et al. 2019; Kremer et al. 2023).

A significant barrier to our understanding of FRBs is their sole detection in the radio band (see, e.g., Chen et al. 2020; Nicastro et al. 2021 for reviews on multiwavelength observations). ¹⁷ This situation is reminiscent of the first two decades of gamma-ray burst (GRB) research when only gamma-ray emission had been detected; it was only through rapid multiwavelength detections of the associated afterglows that the progenitors and physics of GRBs were eventually uncovered. ¹⁸

In the same vein, rapid and deep optical follow-up of FRBs may shed light on their physical mechanisms. FRB models predict a wide range of possible luminosities and timescales for optical transient counterparts, ranging from no emission at all, to luminous (≳10⁴¹ erg s⁻¹) afterglows on a millisecond timescale, to fainter (≲10³⁹ erg s⁻¹) afterglows on timescales of minutes to hours (e.g., Lyubarsky 2014; Beloborodov 2017; Metzger et al. 2019; Yang et al. 2019; Margalit et al. 2020a, 2020b; Beloborodov 2020). Previous optical follow-up attempts have suffered from the combination of FRB poor localizations, large distances, delayed announcements of bursts, and a limited sample of repeating FRBs, resulting in only weak constraints (e.g., ≲10⁴⁵ erg s⁻¹ over a millisecond timescale to ≲10⁴³ erg s⁻¹ over a minute timescale; Hardy et al. 2017; MAGIC Collaboration et al. 2018; Andreoni et al. 2020; Niino et al. 2022); dedicated monitoring of a single burst from the well-localized repeating FRB 20180916B (d_L ≈ 150 Mpc; Marcote et al. 2020) placed marginal constraints (≲10⁴⁰ erg s⁻¹ over minute timescale) on models such as the synchrotron maser with high burst energies and circumburst densities (Kilpatrick et al. 2021).

Here, we report the largest set of optical constraints to date, for a sample of eight well-localized repeating FRBs (including the Galactic SGR 1935+2154) and seven well-localized non-repeating FRBs, using an extensive set of archival data, as well as our own dedicated follow-up observations of the nearby repeating FRB 20200120E and simultaneous observations of the newly discovered and highly active FRB 20220912A (McKinven & CHIME/FRB Collaboration 2022), the most sensitive simultaneous observations to date for any extragalactic FRB. The paper is structured as follows. We summarize the FRB sample, optical observations, and data reduction in Section 2. In Section 3, we analyze and discuss the optical luminosity, flux, and fluence limits in the context of the FRBs' radio properties, and compare these to theoretical models. We summarize our findings and conclude with a future outlook in Section 4.

2.1. Fast Radio Burst Sample

2.2. Optical Observations

For each FRB in our sample, we obtained optical photometry from the ZTF forced-photometry service ²² (Masci et al. 2019) in the g, r, and i bands, and the ATLAS forced photometry server ²³ (Shingles et al. 2021) in the c and o bands for the entire time interval spanning all of the radio bursts for each FRB (i.e., from the first to latest measured bursts). The detection significance (σ) of optical measurements was determined from the ratio of measured flux (f) to its error (f_err). For any measurements above 3σ, we visually inspected the difference images and found that all were due to subtraction artifacts (e.g., bad focus, world coordinate system offset, shutter problems). Thus, we calculate the 3σ upper limits as $-2.5\,{\mathrm{log}}_{10}(3\times {f}_{\mathrm{err}})+\mathrm{ZP}$, where "ZP" is the zero point in the AB magnitude system.

In addition, we carried out dedicated monitoring observations of the nearby FRB 20200120E in M81 (Bhardwaj et al. 2021; Kirsten et al. 2022a) with 300 s exposures simultaneously in the g, r, i, and z bands from 2021 March 19 to 2022 May 18 (UT dates are used throughout) roughly every 10 days with MuSCAT3 (Narita et al. 2020) on the 2 m Faulkes Telescope North (Hawaii, USA) in the Las Cumbres Observatory (LCO; Brown et al. 2013) network. These images have typical g r i z-band 3σ limiting magnitudes of 22.8, 22.9, 22.3, and 22.0, respectively. The March 19 observations, during which no FRBs were announced, were used as template images, and image subtraction was performed using lcogtsnpipe ²⁴ (Valenti et al. 2016), a PyRAF-based photometric reduction pipeline, and PyZOGY ²⁵ (Guevel & Hosseinzadeh 2017), an implementation in Python of the subtraction algorithm described in Zackay et al. (2016). The g r i z-band data were calibrated to AB magnitudes using the 13th Data Release of the Sloan Digital Sky Survey (SDSS; Albareti et al. 2017).

For the recently discovered highly active FRB 20220912A (McKinven & CHIME/FRB Collaboration 2022), we carried out monitoring observations during the CHIME observing windows ²⁶ with three facilities: a series of 40 s exposures and a series of 60 s exposures in the r band with KeplerCam (Szentgyorgyi et al. 2005) on the 1.2 m Telescope at the Fred Lawrence Whipple Observatory (FLWO; Arizona, USA), reaching typical 3σ limiting magnitudes of 20.5 and 21.1, respectively; a series of 400 s exposures in the r band with the Sinistro camera on the 1 m telescope at the McDonald Observatory (Texas, USA) in the LCO network, reaching a typical 3σ limiting magnitude of 22.6; and a series of 15 s exposures in the r band with Binospec (Fabricant et al. 2019) on the 6.5 m MMT Observatory (Arizona, USA), reaching a typical 3σ limiting magnitude of 23.2. In total, we obtained 10 simultaneous optical observations during 13 FRB detections: nine with KeplerCam ²⁷ for the two Deep Synoptic Array (DSA) detections on 2022 October 18 and 25 (Ravi et al. 2022a) and the nine CHIME detections on October 20, 25, and 30 and November 7 and 9 (CHIME VOEvent Service ²⁸ ); and one with LCO for the two CHIME detections on October 22. These KeplerCam and LCO simultaneous exposures, as well as a nearly simultaneous Binospec exposure 0.4 s after a CHIME detection, are shown in Figure 1. Due to the uncertainty (≲a few seconds) in the shutter opening time stamps (from the open command being issued to the shutter being fully opened), the nearly simultaneous Binospec exposure may indeed be simultaneous. We note this caveat in the following analysis and discussion wherever appropriate.

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Using a custom photometry pipeline, the KeplerCam, LCO, and Binospec data were reduced and calibrated to AB magnitudes from the Pan-STARRS1 ²⁹ (PS1; Chambers et al. 2016) Data Release 2 (DR2; Flewelling et al. 2020). Cosmic rays were identified and masked using Cosimic-CONN ³⁰ (Xu et al. 2021, 2021, 2022), and image subtraction was performed against PS1 template images using PyZOGY. For each simultaneous exposure, we stacked it with the subsequent exposures in the same series to obtain deeper limits (typical limiting magnitudes of 21.5 and 23 for KeplerCam and LCO observations, respectively). An example image subtraction is shown in Figure 1 for one of the simultaneous KeplerCam images. We do not detect any transient source in the subtracted KeplerCam, LCO, and Binospec images within any of the FRB localization regions. Thus, we report their 3σ upper limits.

We correct all optical limits for MW extinction assuming the Fitzpatrick (1999) reddening law with R_V = 3.1. After correcting the DM- and frequency-dependent time delay (see Equation (1) of Cordes & Chatterjee 2019) and referencing all the radio and optical measurements to the solar system barycenter (Eastman et al. 2010), ³¹ we find the temporally closest radio burst for each optical limit with respect to the optical exposure midpoint to determine the time difference.

3.1. Optical Luminosity Limits

None of our simultaneous and follow-up observations or the archival observations have led to a detected optical counterpart. We plot all of the resulting KeplerCam, LCO, and Binospec luminosity limits, along with the archival and literature sample in Figure 2. Most of the untargeted ZTF and ATLAS observations occur ≳10⁴ s before and/or after radio bursts, with a wide luminosity limit range of ∼10³⁵–10⁴⁵ erg s⁻¹; the deepest limits are for the Galactic magnetar SGR 1935+2154, given the much smaller distance compared to the other extragalactic FRBs. An untargeted ZTF r-band observation for FRB 20200120E (Andreoni et al. 2021) and the targeted (but nonsimultaneous) gri-band observations with ARCTIC on the Apache Point Observatory (APO) 3.5 m telescope (Huehnerhoff et al. 2016) for FRB 20180916B (Kilpatrick et al. 2021) probe a luminosity range of ∼2 × 10³⁸–4 × 10⁴⁰ erg s⁻¹ within ∼10³ s of radio bursts.

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On a shorter timescale, several targeted high-speed simultaneous observations—by ULTRASPEC on the 2.4 m Thai National Telescope (TNT; Tulloch & Dhillon 2011; Dhillon et al. 2014) for FRB 20121102A (Hardy et al. 2017); the central pixel of the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescopes (Lucarelli et al. 2008; Hassan et al. 2021) for FRB 20121102 (MAGIC Collaboration et al. 2018); and Tomo-e Gozen on the Kiso 105 cm Schmidt telescope (Sako et al. 2018) for FRB 20190520B (Niino et al. 2022)—span a temporal range ∼1–10 ms before/after radio bursts with a luminosity upper limit range of ∼10⁴⁵–10⁴⁷ erg s⁻¹ in a single exposure (longer and deeper stacked exposures are also shown in Figure 2). In the ZTF archival search, we also find a simultaneous 30 s r-band observation of FRB 20121102A with a luminosity limit of ∼6 × 10⁴³ erg s⁻¹.

Among the simultaneous optical observations, our KeplerCam and LCO r-band limits for FRB 20220912A are the deepest to date in terms of luminosity for the extragalactic FRBs, ∼(0.3–2.9) ×10⁴² erg s⁻¹ with 30–400 s exposures (i.e., excluding the Burst Observer and Optical Transient Exploring System, BOOTES, Z-band limit of ∼1.8 × 10³⁵ erg s⁻¹ with a 60 s exposure for the Galactic SGR 1935+2154; Lin et al. 2020). Our nearly simultaneous Binospec limit for FRB 20220912A is at ∼2 × 10⁴¹ erg s⁻¹ with a 15 s exposure started at 0.4 s after a burst.

3.2. Optical-to-Radio Flux and Fluence Ratio Limits

To place the optical limits in the context of the individual FRB burst properties, we plot the ratio of optical flux limit to FRB radio fluence, f_opt/F_radio, in Figure 3. We make this parameter choice because the optical burst duration (t_opt) is not known. If the fluence measurement of a particular radio burst is not yet published, it is assumed to be the mean of the fluence distribution of the relevant repeating FRB (e.g., the recently discovered FRB 20220912A). We find that the range of flux-to-fluence ratio limits is ∼10⁻⁹–0.1 ms⁻¹, on a timescale of ≳10³ s.

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If we make a conservative assumption that the optical counterpart duration is t_opt ≈ Δt, where Δt is the time delay between an FRB and an optical observation, we find that all of the targeted simultaneous observations lie below the critical line of f_optΔt/F_radio ≈ F_opt/F_radio = 1. On the other hand, nearly all of the untargeted and archival observations are well above the F_opt/F_radio = 1 line (Figure 3), meaning that they provide weak constraints for any model in which the energy release per frequency in the optical band is at most comparable to that in the radio bursts; exceptions are some nonsimultaneous APO and untargeted ZTF observations for FRBs 20180916 and 20220912A, respectively. Our nearly simultaneous Binospec limit is at f_opt/F_radio ≲ 10⁻⁸ ms⁻¹ (or F_opt/F_radio ≲ 10⁻⁴) at Δt ≈ 0.4 s, which is the deepest for any FRBs on this timescale.

Among the simultaneous optical observations, our KeplerCam and LCO r-band limits for FRB 20220912A are the deepest to date in terms of f_opt/F_radio for any extragalactic FRB, and indeed comparable to limits for the Galactic SGR 1935+2154, with f_opt/F_radio ≲ 10⁻⁷ ms⁻¹. In terms of fluence ratios, our observations place a limit of F_opt/F_radio ≲ 10⁻³. Our nearly simultaneous Binospec limit would be the deepest if it were indeed simultaneous given the aforementioned shutter timing uncertainty. We stress that these fluence ratio limits are lower than the observed values for the Crab and Geminga pulsars (e.g., Danilenko et al. 2011; Bühler & Blandford 2014), which may suggest a different emission mechanism (although pulsars with lower fluence ratios have also been observed; see, e.g., Niino et al. 2022 for a discussion for FRB 20190520B in this context).

3.3. Constraints on Fast Optical Burst Models

To constrain possible fast optical bursts on a comparable timescale to the radio bursts, we define an effective optical flux limit on a timescale, t_opt (see also Lyutikov & Lorimer 2016):

$$\begin{eqnarray}&&{f}_{\mathrm{eff},\mathrm{opt}}={f}_{\mathrm{opt}}\displaystyle \frac{{T}_{\exp }}{{t}_{\mathrm{opt}}},\end{eqnarray} \tag{ 1 }$$

where ${T}_{\exp }$ is the exposure time. For the sample of FRBs with simultaneous optical observations, we show f_eff,opt/f_radio as a function of t_opt in Figure 4. The previously published high-speed observations of FRBs 20121102A and 20190520B only probe f_eff,opt/f_radio ≳ 0.1 on millisecond timescales, and reach f_eff,opt/f_radio ∼ 0.01 only on $\gtrsim$ second timescales due to the shallow integrated flux limit (i.e., apparent magnitude limit).

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On the other hand, our KeplerCam and LCO observations for FRB 20220912A are far more sensitive, reaching f_eff,opt/f_radio ≲ 0.02 on a millisecond timescale, and ≲3 × 10⁻⁵ on a second timescale. These limits are only an order of magnitude higher than the limits for the Galactic SGR 1935+2154. Our nearly simultaneous Binospec observation for FRB 20220912A reaches f_eff,opt/f_radio ≲ 10⁻⁶ on a second timescale (and ≲10⁻³ on a millisecond timescale if it were indeed simultaneous), which is on the same order as the SGR 1935+2154 limits.

We also plot in Figure 4 broad ranges of some optical burst models from Yang et al. (2019). ³² In these models the subsequent optical bursts to FRBs originate from several inverse-Compton scattering processes involving a highly magnetized central source, such as a young pulsar or magnetar. One-zone models (e.g., pulsar magnetosphere and maser outflow) are expected to have t_opt ≈ t_FRB, while two-zone models could result in a much longer timescale for the optical emission given the larger scattering region than FRB emission region (e.g., ∼5000 s for the pulsar nebula model; Yang et al. 2019). The optical constraints for FRBs 20121102A and 20190520B from previous observations barely reach the upper end of the pulsar nebula model with t_opt ∼ 0.1–10 s. Those of SGR 1935+2154 are well within the model predictions for pulsar magnetosphere and nebula (see also Lin et al. 2020). For the first time for an extragalactic FRB, our limits for FRB 20220912A also reach the model prediction ranges. Within these models, these limits provide meaningful constraints on the magnetic field of B ≲ 10¹⁴ G for magnetars or the spin period of P ≲ 0.01 s for young pulsars.

In Figure 4, we also show potential constraints from high-speed observations with a large-aperture telescope, specifically the Subaru High-Speed Suprime-Cam (HSSC), a planned upgrade for the Suprime-Cam instrument. These potential future observations can provide limits of f_eff,opt/f_radio ≲ 0.01–10⁻⁴ on millisecond to second timescales for FRBs 20121102A and 20190520B, reaching the pulsar magnetosphere and pulsar nebula model parameter space. For FRB 20220912A and SGR 1935+2154, these observations would probe f_eff,opt/f_radio ≲ 10⁻⁴–10⁻⁵ on a millisecond timescale to 10⁻⁷–10⁻⁸ on a second timescale, reaching even to the maser outflow model parameter space.

3.4. Constraints on the Synchrotron Maser Model

To place the luminosity limits on a longer timescale into context, we compare them with theoretical light curves from the synchrotron maser model (Metzger et al. 2019; Margalit et al. 2020a, 2020b). In this model, relativistic plasma ejected from a central engine (e.g., a magnetar) creates a shock in the external magnetized medium (produced in previous flare events), resulting in an FRB from synchrotron maser emission (Plotnikov & Sironi 2019). The model predicts that a broadband synchrotron afterglow will follow the FRB and peak in gamma- to X-rays on a millisecond timescale and in optical on minute to hour timescales. We provide details of the model (including the relevant equations) in Appendix B and show model light curves in Figure B1. Assuming an external medium with a constant (shell-like) density distribution, the afterglow light curves are parameterized by the flare energy (${E}_{\mathrm{flare}}$) ejecting the relativistic plasma and the external density (n_ext) at the shock front; we note that the density structure could in reality be more complex, either wind-like (∝r⁻²) or a combination of multiple structures (e.g., see Cooper et al. 2022 for the case of SGR 1935+2154).

We explore ${E}_{\mathrm{flare}}$ and n_ext ranges of 10³⁷–10⁵⁰ erg and 10–10⁷ cm⁻³, respectively, for each FRB, except the Galactic SGR 1935+2154, where we use a lower ${E}_{\mathrm{flare}}$ bound of 10³² erg. We calculate a model light curve (in terms of specific luminosity at each optical filter effective wavelength) for every combination of ${E}_{\mathrm{flare}}$ and n_ext and compare each optical limit with the integrated average over the exposure time. If the model light curve is brighter than the optical limit, we consider the specific combination of ${E}_{\mathrm{flare}}$ and n_ext parameter space as constrained. The results are shown in Figure 5, along with FRB-based estimates of ${E}_{\mathrm{flare}}$ and n_ext for each burst (see Equations (B6)–(B8)). The model light curves, and thus the optical constraints, are more sensitive to ${E}_{\mathrm{flare}}$ than to n_ext since the characteristic synchrotron frequency, above which the light curves decline exponentially, is set by ${E}_{\mathrm{flare}}$ (see Equations (B1)–(B5)).

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As shown in Figure 5, the existing optical constraints already reach the high-${E}_{\mathrm{flare}}$ ends of the distributions for FRB 20180916B (≳10⁴⁴ erg; see also Kilpatrick et al. 2021) and SGR 1935+2154 (≳10³⁹ erg; see also Cooper et al. 2022). The combination of our simultaneous KeplerCam and LCO observations, and nearly simultaneous deep Binospec observation (with only a 0.4 s delay), are the main drivers for constraining the FRB 20220912A parameter space (≳10⁴⁵ erg) covering ≈65% of its radio bursts observed to date (the ones with published flux/fluence information).

In Figure 5, we also show the potential constraints from future observations. Follow-up 60–300 s observations with 1–5 minutes delay using a 1 m class telescope (e.g., KeplerCam and LCO; limiting magnitude of 20–22) have the potential to reach the high ${E}_{{\rm{flare}}}$ end of the distribution of FRB 20201124A $(\sim {10}^{46}erg)$. Similarly, simultaneous 0.1–1 s observations using an 8 m class telescope (e.g., Subaru HSSC) could potentially constrain the high-${E}_{\mathrm{flare}}$ end and mid-${E}_{\mathrm{flare}}$ range of the distributions of FRB 20200120E (∼10³⁹ erg) and SGR 1935+2154 (∼10³⁶ erg), respectively, if we could target them in an active phase.

We presented the most constraining limits on transient optical counterparts of FRBs to date, from dedicated simultaneous observations of 13 bursts from the repeating FRB 20220912A, and a nearly simultaneous observation with a 6.5 m MMT/Binospec delayed by only 0.4 s (which may indeed be simultaneous given the shutter timing uncertainty). We further presented our dedicated follow-up observations, and compiled all available serendipitous archival and published observations following bursts from a sample of eight repeating FRBs (including the Galactic SGR 1935+2154) and seven nonrepeating FRBs. This data set, and in particular our simultaneous observations of FRB 20220912A, provides the largest study to date of optical emission associated with FRBs. None of the FRBs studied here presented detectable transient optical counterparts. Our key findings are as follows:

• 1.  
  Nearly all archival optical observations have a delay of ≳10⁴ s relative to the time of bursts, while targeted observations have shorter and even up to no delays providing some constraining limits.
• 2.  
  Previous simultaneous observations provided optical luminosity limits of ≲10⁴⁵ erg s⁻¹ (with the exception of SGR 1935+2154 with ≲10³⁵ erg s⁻¹), while our simultaneous KeplerCam and LCO observations provide limits of ≲10⁴² erg s⁻¹, a three orders of magnitude improvement. Our nearly simultaneous Binospec observation reaches a limit of ≲2 × 10⁴¹ erg s⁻¹.
• 3.  
  Normalizing the optical fluence limits (using the time delay as a proxy for t_opt) by the radio fluences, most archival observations have F_opt/F_radio ≳ 1, and therefore place only weak constraints on the relative energy per frequency in the optical and radio. On the other hand, our simultaneous KeplerCam and LCO observations and nearly simultaneous deep Binospec observations place more meaningful limits of F_opt/F_radio ≲ 10⁻³ and ≲10⁻⁴, respectively (even comparable to/deeper than the limits obtained for SGR 1935+2154).
• 4.  
  Comparing the simultaneous limits (normalized by radio flux), we find that previous observations did not constrain models for simultaneous optical bursts (with the exception of one observation of SGR 1935+2154), while our KeplerCam and LCO and nearly simultaneous Binospec observations of FRB 20220912A place the first meaningful constraints on model predictions, ruling out portions of the parameter space for some models.
• 5.  
  Interpreting the optical luminosity limits in the context of the synchrotron maser model, and comparing to the distributions of ${E}_{\mathrm{flare}}$ and n_ext inferred from the radio bursts for each repeating FRB, we find that most optical limits are not constraining (except the one limit for SGR 1935+2154), but our simultaneous and targeted observations of FRB 20220912A rule out the bulk of the parameter space for this model.

Given the estimated high burst rate of FRB 20220912A (∼a few hundreds per hour; Kirsten et al. 2022b; Bhusare et al. 2022; Feng et al. 2022; McKinven & CHIME/FRB Collaboration 2022; Zhang et al. 2022), and the fact that most searches have not published arrival times for their detected bursts, it is possible that we have simultaneous coverage for additional bursts (including multiple bursts in a single exposure added coherently, as in the KeplerCam and LCO exposures), which would place tighter constraints on the fast optical burst and synchrotron maser models. This will be explored once all the FRB measurements (e.g., arrival times, duration, flux, and fluence) become public. Indeed, to enable this type of work on a rapid timescale, we advocate for FRB search efforts to make these basic properties public in real time.

We further investigate the potential of future follow-up and coordinated simultaneous observations using 1–8 m class telescopes on a wide range of timescales from milliseconds to minutes. We find that these observations have the potential to better constrain optical emission from FRBs compared to the bulk of serendipitous archival observations. In particular, based on the experience and constraining limits from our KeplerCam, LCO, and Binospec observations, as well as previous targeted observations (e.g., Hardy et al. 2017; MAGIC Collaboration et al. 2018; Kilpatrick et al. 2021; Niino et al. 2022), we advocate for an approach of simultaneous monitoring of FRBs during CHIME (or other facility) observing windows, especially when repeating FRBs are in a particularly active phase.

We are grateful to Charles Kilpatrick, Wenbin Lu, Lachlan Marnoch, Sandro Mereghetti, Eli Waxman, and Luca Zampieri for useful discussions and comments, to Joscha Jahns for providing Arecibo burst information of FRB 20121102A, to Vikram Ravi for providing DSA burst information of FRB 20220912A, to Daniel Fabricant, Jan Kansky, and Benjamin Weiner for scheduling the MMT Binospec observations and providing the instrument details, and to Griffin Hosseinzadeh for providing the basis of our custom photometry pipeline.

The Berger Time-Domain research group at Harvard is supported by the NSF and NASA. I.A. is a CIFAR Azrieli Global Scholar in the Gravity and the Extreme Universe Program and acknowledges support from that program, from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement No. 852097), from the Israel Science Foundation (grant No. 2752/19), from the United States—Israel Binational Science Foundation (BSF), and from the Israeli Council for Higher Education Alon Fellowship.

This work makes use of observations from KeplerCam on the 1.2 m telescope at the Fred Lawrence Whipple Observatory. Observations reported here were obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona.

This work makes use of observations from the Las Cumbres Observatory global telescope network. This paper is based in part on observations made with the MuSCAT3 instrument, developed by the Astrobiology Center and under financial support by JSPS KAKENHI (grant No. JP18H05439) and JST PRESTO (grant No. JPMJPR1775), at Faulkes Telescope North on Maui, H i, operated by the Las Cumbres Observatory. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Haleakalā has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from the mountain.

This research has made use of the NASA Astrophysics Data System (ADS), the NASA/IPAC Extragalactic Database (NED), and NASA/IPAC Infrared Science Archive (IRSA, which is funded by NASA and operated by the California Institute of Technology), and IRAF (which is distributed by the National Optical Astronomy Observatory, NOAO, operated by the Association of Universities for Research in Astronomy, AURA, Inc., under cooperative agreement with the NSF).

We acknowledge use of the CHIME/FRB Public Database and the VOEvent Service, provided at https://www.chime-frb.ca/ by the CHIME/FRB Collaboration.

This work has made use of data from the Zwicky Transient Facility (ZTF). ZTF is supported by NSF grant No. AST-1440341 and a collaboration including Caltech, IPAC, the Weizmann Institute for Science, the Oskar Klein Center at Stockholm University, the University of Maryland, the University of Washington, Deutsches Elektronen-Synchrotron and Humboldt University, Los Alamos National Laboratories, the TANGO Consortium of Taiwan, the University of Wisconsin at Milwaukee, and Lawrence Berkeley National Laboratories. Operations are conducted by COO, IPAC, and UW. The ZTF forced-photometry service was funded under the Heising-Simons Foundation grant No. 12540303 (PI: Graham).

This work has made use of data from the Asteroid Terrestrial-impact Last Alert System (ATLAS) project. ATLAS is primarily funded to search for near-Earth asteroids through NASA grant Nos. NN12AR55G, 80NSSC18K0284, and 80NSSC18K1575; byproducts of the NEO search include images and catalogs from the survey area. This work was partially funded by Kepler/K2 grant No. J1944/80NSSC19K0112 and HST grant No. GO-15889, and STFC grant Nos. ST/T000198/1 and ST/S006109/1. The ATLAS science products have been made possible through the contributions of the University of Hawaii Institute for Astronomy, the Queens University Belfast, the Space Telescope Science Institute, the South African Astronomical Observatory, and The Millennium Institute of Astrophysics (MAS), Chile.

The PS1 and the PS1 public science archives have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, NASA under grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, NSF grant No. AST-1238877, the University of Maryland, Eotvos Lorand University, the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

Facilities: ADS - , ATLAS - , IRSA - , FLWO (KeplerCam) - , LCO (MuSCAT3 - , Sinistro) - , MMT (Binospec), NED - , ZTF - .

Software: Astropy Astropy Collaboration et al. (2018), atlas-fp (https://gist.github.com/thespacedoctor/86777fa5a9567b7939e8d84fd8cf6a76), barycorr (Eastman et al. 2010;https://github.com/tronsgaard/barycorr), Cosimic-CONN (Xu et al. 2021, 2021, 2022), dustmaps (Green 2018), lcogtsnpipe (Valenti et al. 2016), Matplotlib (Hunter 2007), NumPy (Oliphant 2006), PyZOGY (Guevel & Hosseinzadeh 2017), SciPy (Virtanen et al. 2020), seaborn (Waskom et al. 2020), SExtractor (Bertin & Arnouts 1996).

We summarize the well-localized non-repeating FRB sample and their references in Table A1. The same luminosity and flux analyses as for the repeating FRBs are performed and shown in Figures A1 and A2, except for the simultaneous flux analysis since no such measurements are available given the unpredictable nature of one-off FRBs. We find that none of the optical limits are particularly constraining. Nevertheless, we also compare the luminosity limits to the light curves from the synchrotron maser model (although its application is somewhat questionable given the one-off nature of these events), concluding that only the very high-${E}_{\mathrm{flare}}$ end (≳10⁴⁸ erg) could be constrained. These constraints are at least three orders of magnitude larger than the FRB-based estimates (where available).

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Table A1. Well-localized Non-repeating FRB Sample

FRB	R.A.	Decl.	Redshift	dLa	AV,MW b	Frequency	DM	Width c	Flux c	Fluence c
	(deg)	(deg)	(z)	(Mpc)	(mag)	(GHz)	(pc cm−3)	(ms)	(Jy)	(Jy ms)
20190608B d	334.01988(1)	−7.89825(8)	0.1178	541	0.125	1.295	338.7(5)	6.0(8)	∼4.3	26(4)
20200430A e	229.70642(8)	+12.3769(3)	0.160	755	0.112	0.8645	380.1(4)	⋯	⋯	35(4)
20190714A f	183.9797(1)	−13.02103(8)	0.2365	1167	0.166	1.2725	504(2)	⋯	⋯	8(2)
20191228A g	344.4304(3)	−29.5941(3)	0.2432	1204	0.065	1.2715	297.5(5)	2.3(6)	∼17	${40}_{-40}^{+100}$
20200906A h	53.4962(1)	−14.0832(2)	0.3688	1946	0.126	0.8645	577.8(2)	6.0(6)	∼9.8	${59}_{-10}^{+25}$
20190614D i	65.07554(8)	+73.70675(8)	0.6	3480	0.371	1.4	959(5)	∼5.0	0.12(1)	0.62(7)
20190523A j	207.0650(1)	+72.4697(6)	0.660	3908	0.050	1.530	760.8(6)	0.42(5)	≳660	≳280

Notes.

^a Calculated from the host redshift assuming a standard ΛCDM cosmology with H₀=71.0 km s⁻¹ Mpc⁻¹, Ω_Λ = 0.7, and Ω_m = 0.3. ^b From Schlafly & Finkbeiner (2011), retrieved via IRSA. ^c If only two of the width (t_FRB), flux (f_radio), and fluence (F_radio) are reported for a particular burst, the third parameter is estimated assuming F_radio ∼ f_radio t_FRB. ^d Localized with ASKAP and the host spectroscopic redshift measured from an archival SDSS spectrum (Day et al. 2020; Macquart et al. 2020). ^e Localized with ASKAP and the host spectroscopic redshift measured with Nordic Optical Telescope (NOT; Heintz et al. 2020; Kumar et al. 2020). ^f Localized with ASKAP and the host spectroscopic redshift measured with Keck (Bhandari et al. 2019; Heintz et al. 2020). ^g Localized with ASKAP and the host spectroscopic redshift measured with Keck (Shannon et al. 2019; Bhandari et al. 2022). ^h Localized with ASKAP and the host spectroscopic redshift measured with Keck (Bhandari et al. 2022). ⁱ Localized with VLA and the host photometric redshift estimated from spectral energy distribution fits (Law et al. 2020). ^j Localized with DSA and the host spectroscopic redshift measured with Keck (Ravi et al. 2019).

A machine-readable version of the table is available.

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With slight modifications, we follow Kilpatrick et al. (2021) for the application of the synchrotron maser model of Metzger et al. (2019), Margalit et al. (2020a), and Margalit et al. (2020b) to their optical limits on the well-localized repeating FRB 20180916B. In this model, the prompt radio emission (i.e., FRB) and afterglow gamma-ray to optical emission originate from the shock interaction between magnetar/pulsar-ejected plasma and the highly magnetized external medium. The characteristic synchrotron frequency (ν_syn) is set by the flare energy (${E}_{\mathrm{flare}}$):

$$\begin{eqnarray}&&h{\nu }_{\mathrm{syn}}({t}_{\mathrm{FRB}})=57\,\mathrm{MeV}{\left(\displaystyle \frac{\sigma }{0.1}\right)}^{1/2}{\left(\displaystyle \frac{{E}_{\mathrm{flare}}}{{10}^{43}\,\mathrm{erg}}\right)}^{1/2}{\left(\displaystyle \frac{{t}_{\mathrm{FRB}}}{\mathrm{ms}}\right)}^{-3/2},\end{eqnarray} \tag{ B1 }$$

where t_FRB is the FRB duration (or width) and σ is the fractional magnetization (see Equations (56) and (57) of Metzger et al. 2019). In this work, we assume a fiducial σ = 0.3 (Plotnikov & Sironi 2019). The time evolution of the synchrotron frequency is as follows:

$$\begin{eqnarray}{\nu }_{\mathrm{syn}}(t)=\left\{\begin{array}{ll}{\nu }_{\mathrm{syn}}({t}_{\mathrm{FRB}}){\left(\displaystyle \frac{t}{{t}_{\mathrm{FRB}}}\right)}^{-1} & \mathrm{for}\ t\ \lt \ {t}_{\mathrm{FRB}}\\ {\nu }_{\mathrm{syn}}({t}_{\mathrm{FRB}}){\left(\displaystyle \frac{t}{{t}_{\mathrm{FRB}}}\right)}^{-3/2} & \mathrm{for}\ t\ \gt \ {t}_{\mathrm{FRB}}\end{array}\right..\end{eqnarray} \tag{ B2 }$$

Assuming a constant (shell-like) external density (n_ext) at the shock front, the cooling frequency (ν_cool) can be expressed as a function of time (see Equations (32) and (60) of Metzger et al. (2019) and also Equation (4) of Kilpatrick et al. 2021):

$$\begin{eqnarray}&&h{\nu }_{\mathrm{cool}}(t)=2.3\,\mathrm{keV}{\left(\displaystyle \frac{\sigma }{0.1}\right)}^{-3/2}{\left(\displaystyle \frac{{n}_{\mathrm{ext}}}{{10}^{3}\,{\mathrm{cm}}^{-3}}\right)}^{-1}{\left(\displaystyle \frac{t}{{10}^{-3}\,{\rm{s}}}\right)}^{-1/2}.\end{eqnarray} \tag{ B3 }$$

Then, the peak luminosity (L_peak) and specific luminosity (L_ν ) can be written as a function of frequency (see Equations (63) and (64) of Metzger et al. 2019):

$$\begin{eqnarray}&&{L}_{\mathrm{peak}}(t)={10}^{45}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\left(\displaystyle \frac{{E}_{\mathrm{flare}}}{{10}^{43}\,\mathrm{erg}}\right){\left(\displaystyle \frac{t}{{10}^{-3}\,{\rm{s}}}\right)}^{-1},\end{eqnarray} \tag{ B4 }$$

$$\begin{eqnarray}\nu {L}_{\nu }(t)=\left\{\begin{array}{ll}{L}_{\mathrm{peak}}{\left(\displaystyle \frac{\nu }{{\nu }_{\mathrm{cool}}}\right)}^{4/3}{\left(\displaystyle \frac{{\nu }_{\mathrm{cool}}}{{\nu }_{\mathrm{syn}}}\right)}^{1/2}\propto {t}^{1/6} & \mathrm{for}\ \nu \lt {\nu }_{\mathrm{cool}}\\ {L}_{\mathrm{peak}}{\left(\displaystyle \frac{\nu }{{\nu }_{\mathrm{sync}}}\right)}^{1/2}\propto {t}^{-1/4} & \mathrm{for}\ {\nu }_{\mathrm{cool}}\lt \nu \lt {\nu }_{\mathrm{syn}}\\ {L}_{\mathrm{peak}}\,{e}^{-(\nu /{\nu }_{\mathrm{syn}}-1)}\propto {t}^{-1}\,{e}^{-{t}^{3/2}} & \mathrm{for}\ {\nu }_{\mathrm{syn}}\lt \nu \end{array}\right.,\end{eqnarray} \tag{ B5 }$$

where we adopt an exponential cutoff above ν_syn, as in Kilpatrick et al. (2021). The time dependence is shown for t > t_FRB. Representative model light curves in the r band (ν = 5 × 10¹⁴ Hz) for various choices of ${E}_{\mathrm{flare}}$ and n_ext are shown in Figure B1.

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From FRB measurements of the radio fluence (F_radio) and frequency (ν_obs), the isotropic radio energy (E_radio) and flare energy can be estimated as

$$\begin{eqnarray}&&{E}_{\mathrm{radio}}=9.5\times {10}^{31}\,\mathrm{erg}\left(\displaystyle \frac{4\pi }{1+z}\right){\left(\displaystyle \frac{{dL}}{\mathrm{Mpc}}\right)}^{2}\left(\displaystyle \frac{{F}_{\mathrm{radio}}\cdot {\nu }_{\mathrm{obs}}}{\mathrm{Jy}\,\mathrm{ms}\cdot \mathrm{GHz}}\right),\end{eqnarray} \tag{ B6 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{E}_{\mathrm{flare}}}{{E}_{\mathrm{radio}}}=3.3\times {10}^{4}{\left(\displaystyle \frac{{f}_{e}}{0.5}\right)}^{-1/5}{\left(\displaystyle \frac{{f}_{\xi }}{{10}^{-3}}\right)}^{-4/5}{\left(\displaystyle \frac{{\nu }_{\mathrm{obs}}\cdot {t}_{\mathrm{FRB}}}{\mathrm{GHz}\cdot \mathrm{ms}}\right)}^{1/5},\end{eqnarray} \tag{ B7 }$$

where f_e and f_ξ are the number density ratio of electrons to ions in the upstream medium and the synchrotron maser efficiency, respectively (see Equation (14) of Margalit et al. 2020a). In this work, we assume fiducial f_e = 0.5 and f_ξ = 10⁻³ (Plotnikov & Sironi 2019). The external density can also be estimated from FRB measurements as

$$\begin{eqnarray}\begin{array}{rcl}{n}_{\mathrm{ext}} & = & 420\,{\mathrm{cm}}^{-3}{\left(\displaystyle \frac{{m}_{\star }}{{m}_{e}}\right)}^{2/15}{\left(\displaystyle \frac{{f}_{e}}{0.5}\right)}^{-11/15}{\left(\displaystyle \frac{{f}_{\xi }}{{10}^{-3}}\right)}^{-4/15}\\ & & \times {\left(\displaystyle \frac{{\nu }_{\mathrm{obs}}}{\mathrm{GHz}}\right)}^{31/30}{\left(\displaystyle \frac{{t}_{\mathrm{FRB}}}{\mathrm{ms}}\right)}^{2/5}{\left(\displaystyle \frac{{E}_{\mathrm{radio}}}{{10}^{40}\mathrm{erg}}\right)}^{-1/3},\end{array}\end{eqnarray} \tag{ B8 }$$

where m_⋆ and m_e are the masses of upstream particles and electrons (see Equation (8) of Margalit et al. 2020b). In this work, we assume a pair plasma (i.e., m_⋆ = m_e ). Then, these FRB-based estimates for ${E}_{\mathrm{flare}}$ and n_ext can be compared with the optical constraints, as in Figure 5.