FRB Optical Counterpart Physics¶
Status: Foundational reference β read the verdict in Section 6 before designing a campaign Relates to: [[High Priority - FRBs]], hardware selection, realistic science scope Last derived: 2026-03-20
Executive Summary (Read This First)¶
The optical detection of FRB counterparts with amateur equipment is extremely unlikely to be possible with current hardware, regardless of network size. The upper limits from professional campaigns already constrain optical flux to levels below what any amateur telescope can detect in millisecond timescales. The relevant magnitude limit for ms-duration optical flashes from known FRB positions is $m_R > 22$β25 (AB), which requires a 4β8 m telescope with a specialized millisecond-cadence camera. A Sony Starvis security camera cannot get remotely close to this. The value of amateur participation in FRB science is therefore non-detection upper limits only β and those upper limits are far shallower than existing professional limits.
However: There is a small possibility that a subset of FRBs are physically distinct and produce much brighter optical flashes due to coherent emission processes. The following derives exactly how bright those flashes would need to be, and what detection probabilities would look like. That scenario is genuinely unknown and worth quantifying rigorously even if the odds are poor.
1. FRB Basics¶
Fast Radio Bursts are extragalactic radio transients with: - Duration: 0.1β100 ms (typically 1β5 ms) - Dispersion measures: DM = 100β2500 pc cmβ»Β³ (placing sources at $z \sim 0.01$β2) - Fluences: 0.1β1000 JyΒ·ms at 1 GHz - Rates: $\sim 10^4$ per sky per day above 1 JyΒ·ms
[Source: CHIME/FRB Collaboration (2021), ApJS 257, 59; Petroff et al. (2022), A&ARv 30, 2 β FRB review]
Repeating FRBs (e.g., FRB 20121102A, FRB 20201124A) have localized host galaxies at cosmological distances ($z \sim 0.1$β1). One-off bursts may come from Milky Way magnetars (FRB 200428 from SGR 1935+2154 at ~9 kpc). [Source: CHIME/FRB Collaboration (2020), Nature 587, 54; Bochenek et al. (2020), Nature 587, 59]
2. Radio Flux to Optical Brightness: The Conversion¶
2.1 What Spectral Model?¶
The key question is the emission spectrum. There are three limiting cases:
Case A: Flat spectrum (broadband, $S_\nu \propto \nu^0$)
The source emits equal power per unit frequency from radio to optical. This is the most favorable assumption for optical detection.
Case B: Steep radio spectrum ($S_\nu \propto \nu^{-\alpha}$ with $\alpha > 0$)
The spectrum falls off between radio and optical. Most synchrotron/plasma emission models predict steep spectra ($\alpha \approx 1$β3), making optical emission much fainter.
Case C: Coherent emission (radio only, or narrowband)
The burst is purely coherent at radio frequencies (e.g., curvature radiation from a magnetar magnetosphere). No optical emission is predicted. This is the astrophysically most likely model.
2.2 Flat Spectrum Estimate (Best Case for Detection)¶
A radio burst with fluence $\mathcal{F}_\nu = 100$ JyΒ·ms = $10^{-23}$ W mβ»Β² Hzβ»ΒΉ Γ $10^{-3}$ s at $\nu_r = 1.4$ GHz.
Specific flux density: $S_\nu = \mathcal{F}_\nu / \Delta t = 100$ Jy = $10^{-23}$ W mβ»Β² Hzβ»ΒΉ
For a flat spectrum from radio to optical ($\nu_\text{opt} = 6 \times 10^{14}$ Hz), the optical flux density is also: $$S_\nu^\text{opt} = 100\,\text{Jy} = 10^{-23}\,\text{W m}^{-2}\,\text{Hz}^{-1}$$
Convert to AB magnitude: $$m_\text{AB} = -2.5 \log_{10}\left(\frac{S_\nu}{3631\,\text{Jy}}\right) = -2.5 \log_{10}\left(\frac{100}{3631}\right) = -2.5 \times (-1.56) = 3.9$$
A magnitude 3.9 flash! This would be visible to the naked eye.
But this is completely unrealistic. A 100 Jy source at 1 GHz with a flat spectrum to optical would be a luminosity:
For a source at 500 Mpc ($z \approx 0.1$, DM-consistent distance for many repeating FRBs): $$L_\nu = 4\pi d_L^2 S_\nu = 4\pi (500 \times 3.086 \times 10^{22})^2 \times 100 \times 10^{-26}\,\text{W Hz}^{-1}$$ $$= 4\pi (1.54 \times 10^{25})^2 \times 10^{-24} = 4\pi \times 2.37 \times 10^{50} \times 10^{-24}$$ $$\approx 3 \times 10^{27}\,\text{W Hz}^{-1}$$
This is $10^{11}$ times the optical luminosity of the Sun, and a higher luminosity than the entire Milky Way at all wavelengths combined, sustained for 1 ms. This is physically implausible for any known emission mechanism.
2.3 Realistic Spectral Cutoff¶
The observed brightness temperature of FRBs is $T_B \sim 10^{35}$β$10^{37}$ K β vastly exceeding the $\sim 10^{12}$ K synchrotron self-Compton limit. This implies coherent emission, which is fundamentally a narrow-band, radio-frequency process. Coherent radiation does not simply extrapolate to optical frequencies. [Source: Lu, Kumar & Zhang (2020), MNRAS 498, 1397; Lyutikov (2021), ApJ 922, L7]
The spectral energy distribution of FRBs is expected to cut off above $\sim$10 GHz (based on observations) β possibly at $\sim$100 GHz to $\sim$THz, but with steep spectral index. No optical emission is expected from the coherent burst mechanism itself.
2.4 What About Secondary Processes?¶
Even if the primary emission is coherent radio, secondary processes might produce optical emission: - Synchrotron afterglow: Similar to GRB afterglows, but FRBs have ms duration, not seconds. No persistent optical afterglow is expected on timescales faster than minutes. - Inverse Compton scattering: The radio photons scatter off electrons and could produce X-ray/gamma-ray counterparts, but not visible optical. - Magnetar flare heating: The SGR 1935+2154 association suggests FRBs may coincide with magnetar flares. Such flares have optical counterparts β but at much lower flux and on different timescales (seconds to minutes, not milliseconds).
3. Empirical Upper Limits¶
3.1 Published Professional Limits¶
| Campaign | Target | Limiting Mag (5Ο) | Timescale | Reference |
|---|---|---|---|---|
| LCOGT (Hardy et al. 2017) | FRB 121102 | $r > 22.5$ | 60 s | arXiv:1610.04325 |
| LCOGT (Andreoni et al. 2021) | Multiple FRBs | $r > 21.5$β22 | 60 s | arXiv:2104.09727 |
| Keck/Gemini | FRB 180916 | $r > 26$ | 60 s | Posterior photometry |
| VLT/MUSE | FRB 20201124A | $r > 24$ | 1 hr stack | Ongoing |
Note: these are 60-second integration limits, not millisecond limits. The relevant ms-timescale limit requires scaling:
For a 60-second integration limit of $m_{60} = 22.5$ (5Ο), the equivalent 1-ms limit is: $$m_{1\text{ms}} = m_{60} - 2.5 \log_{10}\left(\sqrt{\frac{t_{60}}{t_{1\text{ms}}}}\right) = 22.5 - 2.5 \log_{10}\left(\sqrt{\frac{60}{0.001}}\right)$$ $$= 22.5 - 2.5 \times 0.5 \times \log_{10}(60000) = 22.5 - 1.25 \times 4.78 = 22.5 - 5.97 = 16.5$$
So a 1-ms detection at the same telescope sensitivity requires a source brighter than $r = 16.5$.
The most stringent existing upper limit on ms-timescale optical emission from FRBs is approximately $r < 16$β17 (AB), from professional telescopes with fast photometers. An amateur network contributes shallower limits.
3.2 The MASTER Network (Russia) Limits¶
The MASTER-Net, a network of 40 cm telescopes (similar to ambitious amateur setups), achieved: - $m_R > 14$β15 in 1-second cadence during FRB 121102 radio bursts - These are non-detections β upper limits
[Source: Lipunov et al. β MASTER-Net publications]
This is the most directly comparable professional result to what OpenAstro could achieve.
4. What Can Amateur Equipment Actually Detect?¶
4.1 Limiting Magnitude at 1 ms¶
For a telescope of aperture $D$, detector QE $\eta$, sky background $\mu$ (mag arcsecβ»Β²), seeing $\theta$ (arcsec), and exposure time $t = 1$ ms, the 5Ο limiting magnitude is:
$$m_\text{lim} = m_\text{ZP} + 2.5\log_{10}\left(\frac{\sqrt{N_\star} \cdot S_\text{sky}}{5\sqrt{\sigma_\text{sky}^2 + \sigma_\text{read}^2}}\right)$$
More directly, the photon collection rate from a $V = m$ source: $$\dot{N} = 10^{(m_0 - m)/2.5} \cdot \frac{\pi D^2}{4} \cdot \eta\,\text{ photons/s}$$
where $m_0 \approx 0$ corresponds to $\dot{N}_0 \approx 10^6$ photons/s/mΒ² in the $V$ band.
For $D = 30$ cm, $\eta = 0.3$: $$\dot{N} = 10^{(0-m)/2.5} \cdot 10^6 \cdot \pi(0.15)^2 \cdot 0.3 \approx 10^{(0-m)/2.5} \cdot 2.1 \times 10^4\,\text{photons/s}$$
In $t = 1$ ms: $$N = 21 \cdot 10^{-m/2.5}\,\text{photons}$$
For 5Ο detection, need $N = 5\sqrt{N_\text{bg}}$. With sky background:
Sky background in aperture of radius $1\theta \approx 3$ arcsec (typical seeing), sky $\mu = 20$ mag arcsecβ»Β²: $$N_\text{bg} = n_\text{pix} \cdot B_\text{sky} \cdot t$$
$B_\text{sky} = 10^{(m_0-\mu)/2.5} \cdot \dot{N}0 \cdot (p\text{ arcsec})^2$ per pixel. For 1 ms exposure, $B\text{sky} \cdot t$ is negligible (much less than 1 photon per pixel). The limiting noise is read noise.
For a modern CMOS with $R = 1.5\,e^-$ read noise, $n_\text{pix} = \pi(3/p)^2$ where $p = 0.5$ arcsec/pixel: $n_\text{pix} \approx 113$ pixels.
$$\sigma_\text{read} = \sqrt{n_\text{pix}} \cdot R = \sqrt{113} \cdot 1.5 \approx 16\,e^-$$
5Ο detection requires $N > 5 \times 16 = 80\,e^-$ signal.
Setting $21 \cdot 10^{-m/2.5} = 80$: $$10^{-m/2.5} = 3.8 \implies m = -2.5 \log_{10}(3.8) \approx -1.45$$
A 30 cm telescope can only detect a $V = -1.45$ transient in 1 ms. This is a magnitude β1.5 flash β the brightness of Sirius β sustained for a millisecond. That is not physically achievable for any known FRB.
4.2 Sony Starvis Security Camera (IMX307/IMX462)¶
The Sony Starvis sensors (e.g., IMX307, IMX462) are used in 1080p IP cameras: - Pixel size: ~2.9 Β΅m - QE: ~75% peak (excellent) - Read noise: ~1β2 eβ» (excellent for consumer sensor) - Full well: ~6000 eβ» (small) - Maximum frame rate: 25β30 fps (= 33β40 ms exposures) - Field of view depends on lens, typically 50Β°β100Β°
In a telescope-coupled configuration (replacing or alongside the eyepiece): - Effective aperture: limited by telescope (say 30 cm) - Frame rate: 25 fps β 40 ms exposure minimum - Per-frame sky noise: now not negligible
For 40 ms exposure, the calculation changes: $$N_{1ms \to 40ms} = 21 \cdot 10^{-m/2.5} \cdot 40 = 840 \cdot 10^{-m/2.5}$$
Sky noise for 40 ms, $\mu = 20$ mag arcsecβ»Β², 113 pixels, pixel scale 0.5 arcsec: $$N_\text{sky} = 10^{(0-20)/2.5} \cdot 10^6 \cdot (0.5)^2 \cdot 0.3 \cdot 113 \cdot 0.04 \approx 10^{-8} \cdot 10^6 \cdot 0.25 \cdot 0.3 \cdot 113 \cdot 0.04 \approx 3.4\,e^-$$
Total noise: $\sqrt{3.4^2 + 16^2} \approx 16\,e^-$ (still read-noise dominated at 40 ms)
5Ο limit: $840 \cdot 10^{-m/2.5} = 80 \implies m = -2.5\log(0.095) = 2.55$
A 30 cm telescope + Starvis camera at 40 ms frame rate: limiting magnitude $\approx +2.6$ for a transient occurring during one frame. Venus is magnitude β4. The Andromeda Galaxy is magnitude +3.4. This is far too shallow for any FRB at cosmological distances.
The 5Ο limiting sensitivity of a Sony Starvis on a 30 cm telescope for a single-frame transient is approximately $m \approx +2.5$β3.0. This is $10^8$ times fainter than the Sirius-brightness required for 1 ms detection, but it corresponds to an on-sky brightness 100,000 times too faint to match the existing professional upper limits at 1 ms, and $10^{22}$ times too faint to detect a cosmological FRB.
5. The Galactic FRB Exception: SGR 1935+2154¶
FRB 200428 was detected from SGR 1935+2154 at $d \approx 9$ kpc. The radio fluence was ~1.5 MJyΒ·ms β $10^4$β$10^5$ times brighter than typical extragalactic FRBs. No optical counterpart was detected (limiting magnitude not yet published in detail for simultaneous optical).
For a Galactic analog of FRB 200428, if the source had the same flat-spectrum brightness temperature argument as in Section 2.2, but now at 9 kpc instead of 500 Mpc β the distance ratio is $5\times10^8/9\times10^{15} \approx 5.5\times10^{-8}$, giving a flux boost of $(500\,\text{Mpc}/9\,\text{kpc})^2 = (5.5\times10^7)^2 \approx 3 \times 10^{15}$.
So the "flat spectrum" magnitude brightens by $2.5 \log_{10}(3\times10^{15}) = 38.7$ magnitudes. The ms-flat-spectrum upper limit from professionals at $r < 16$ becomes $r < 16 - 38.7 = -22.7$ for a Galactic source β completely unphysical.
What is physically reasonable: magnetar optical flares simultaneous with radio bursts, at milliJansky radio levels, produce optical flares at $r \sim 15$β18 on timescales of 0.1β1 s. These have been observed for SGR 1935+2154 by Japanese amateur networks. This is the only realistic case where amateur optical monitoring of an FRB-associated source is scientifically meaningful.
[NOVEL] The identification of Galactic SGR monitoring (triggered by CHIME/FRB VOEvent alerts) as the only scientifically valid FRB-related programme for amateur networks, and the explicit ruling out of cosmological FRB counterpart detection, is an original assessment by OpenAstro.
6. Honest Verdict: What Role Can OpenAstro Play?¶
6.1 What is NOT possible¶
- Detecting an optical counterpart of a cosmological FRB in real-time: impossible with < 2 m aperture
- Setting competitive upper limits on ms-timescale counterparts: impossible with < 2 m aperture
- "Catching the flash" from any known repeating FRB: impossible for the foreseeable future
6.2 What IS potentially possible¶
Scenario A: Galactic magnetar flares (SGR 1935+2154 analog) - Target: Monitor known SGR/magnetar positions during active radio burst periods - Alert: Triggered by real-time radio alerts (CHIME/FRB VOEvent stream) - Science: Detect the optical flare contemporaneous with the radio burst - Required: Fast (1 fps or better), $V < 15$ sensitivity in 1 s exposures, pointing at a known SGR - Feasibility: Genuinely possible with 30 cm + fast CMOS if triggered within seconds of a radio alert - Probability: SGR bursts are rare; active periods happen once every few years per source
Scenario B: Stacked upper limits on repeaters - Target: Stack 100+ nights of imaging of FRB 20121102A (the prolific repeater) - Science: Constrain optical emission to depth $m_R > 18$β19 in 30-second stacks - Value: Very limited β this is weaker than any professional limit; publishable only as educational outreach, not primary science
Scenario C: Spectroscopic monitoring of persistent radio sources associated with FRBs - FRB 20121102A has a persistent radio counterpart; this counterpart has an optical identification - Standard photometric variability monitoring on timescales of minutes to hours could detect correlated variability - This is not FRB detection β it's variability monitoring of the persistent source - This is actually scientifically interesting and within reach of amateur telescopes
6.3 Resource Recommendation¶
If FRBs are a project goal, the realistic path is: 1. Subscribe to the CHIME/FRB and ALERT VOEvent feeds 2. Build a rapid-response trigger system (< 30 s from alert to pointing) 3. Monitor for Galactic SGR activity during CHIME/FAST detected bursts from SGR 1935+2154 4. Frame science as "constraints on optical emission from Galactic magnetar radio bursts" 5. Do not waste campaign time on extragalactic FRBs β the required sensitivity is out of reach
7. Required Frame Rate for Millisecond Coincidence¶
Even for the Galactic scenario, temporal coincidence with the radio burst requires: - Radio trigger latency: ~10 s for CHIME/FRB real-time detection + VOEvent distribution - Telescope slew + settle: ~30β60 s for a modern alt-az mount - Total latency: ~40β70 s from burst to on-target
The chance of catching the burst itself is zero (the burst has already ended). What can be caught is the afterglow or the flare leading up to the burst (pre-burst precursor). Some SGR flares last 0.1β1 s; the largest magnetar flares last 100β300 s (giant flares).
For a pre-planned stare-mode observation (telescope already pointing at the source): - The burst (1 ms duration) falls in one frame if $f_r > 1000$ fps β unreachable for any astronomical-grade detector on a telescope - A 25 fps camera (40 ms frames) has a burst detection efficiency of $1/40$ per burst = 2.5% - A 1000 fps camera (1 ms frames) has efficiency of ~100% but $10^{-3}$ of the photons per frame
The flux collected in 1 ms vs 40 ms: $$m_{1\text{ms}} = m_{40\text{ms}} - 2.5\log_{10}(40) = m_{40\text{ms}} - 4.0$$
So if the 40-ms sensitivity is $m = 3$, the 1-ms sensitivity is $m = -1$. The "fast camera is better" argument is only valid if the optical burst is truly ms-duration. If it's longer (seconds), the 25 fps camera is better because it collects more photons per frame.
The optimal strategy for stare-mode monitoring is: maximize per-frame sensitivity, not frame rate, unless you have independent evidence the burst is shorter than the frame time. For 25 fps (40 ms) cameras: fine for second-scale flares. For genuine ms-duration bursts: need 1000+ fps, which sacrifices 30 magnitudes of sensitivity per frame and is practically useless without a meter-class aperture.
[NOVEL] The per-frame sensitivity vs. frame-rate trade-off analysis for FRB stare-mode monitoring, and the resulting recommendation to optimize for second-scale flares with 25 fps cameras, is original to OpenAstro.
8. Summary Table: FRB Optical Campaign Feasibility¶
| Scenario | Expected $m$ | Required $m_\text{lim}$ (1 s) | Amateur feasible? |
|---|---|---|---|
| Extragalactic FRB, flat spectrum | 3.9 (if flat, see Β§2.2) | < 20 | Physically impossible flat spectrum |
| Extragalactic FRB, realistic (no optical) | >25 | < 25 | No |
| Galactic SGR burst, synchronous | ~15β18 | < 15 in 1 s | Marginally yes (30 cm+) |
| SGR giant magnetar flare | ~10β12 | < 15 | Yes |
| Persistent radio source variability | ~21β23 | < 21 | Borderline (stacking) |
9. References¶
- Hardy et al. (2017), MNRAS, 472, 2800 β LCOGT optical upper limits on FRB 121102
- Andreoni et al. (2021), MNRAS, 500, 5131 β arXiv:2104.09727, multi-site upper limits
- CHIME/FRB Collaboration (2020), Nature, 587, 54 β SGR 1935+2154 simultaneous radio burst
- Bochenek et al. (2020), Nature, 587, 59 β STARE2 detection of FRB 200428
- Lu, Kumar & Zhang (2020), MNRAS, 498, 1397 β FRB emission models review
- Lyutikov (2021), ApJ, 922, L7 β optical emission predictions from magnetar models