Evryscope and K2 Constraints on TRAPPIST-1 Superflare Occurrence and Planetary Habitability

The Evryscope consists of 22 small telescopes housed in a single dome known as "the mushroom," arranged for coverage of almost the entire Southern sky (Law et al. 2015). From its location at Cerro-Tololo Inter-American Observatory (CTIO), the Evryscope images its 8520 square degree field of view every two minutes. The system takes images in the g' band with a typical dark-sky limiting magnitude of g' = 16 and a resolution of 13'' per pixel (Ratzloff et al. 2019). Each night, the Evryscope tracks the sky continuously for two hours as it takes images, then ratchets back to its original position and resumes tracking for another two hours, repeating throughout the night. This cycle yields an average of ∼6 hr of continuous monitoring across the visible sky.

A custom pipeline analyzes the Evryscope data set at real-time rates (Law et al. 2016). With each two-minute exposure, each camera takes a 30 Mpx image, which is saved as a FITS file and calibrated using a custom wide-field solver. The background is modeled and subtracted, then forced-aperture photometry is extracted based on known source positions in a reference catalog. Light curves are then generated for approximately 15 million sources across the Southern sky by differential photometry in small regions of the sky, using carefully selected reference stars and a range of apertures. Residual systematics are removed using two iterations of the SysRem detrending algorithm (Tamuz et al. 2005).

The Evryscope data set contains 9210 images centered on the position of TRAPPIST-1, spanning 2016 June–2018 June. Fewer images exist for TRAPPIST-1 than for most stars in the Evryscope data because of TRAPPIST-1's location in the sky: at a decl. of −5°, TRAPPIST-1 is near the northern edge of the Evryscope's field of view, where there is less camera coverage than for other sources. From the Evryscope's location at CTIO, TRAPPIST-1 is observable from mid-June to late November. Given the observing constraints, images of TRAPPIST-1's position were taken at two-minute cadence for an average of two hours on each observable night. TRAPPIST-1 was observed for a total of 170 nights during the two years of Evryscope coverage, or 12.8 days continuous-equivalent over two years.

TRAPPIST-1 is not bright enough to be visible in Evryscope data when quiescent; at magnitude g' = 19.3 (Chambers et al. 2016), TRAPPIST-1 is much dimmer than the typical Evryscope limiting magnitude of g' ≈ 16. However, a sufficiently large flare would increase TRAPPIST-1's brightness to match or exceed the sky background in Evryscope data. Flares of 3–11 mag have been observed from mid- to late M-dwarfs (Schmidt et al. 2016; Paudel et al. 2018). Previous flare searches with the Evryscope have detected a number of flares in this amplitude range (Howard et al. 2019). If originating from TRAPPIST-1, such flares would be visible in Evryscope images of the star; Section 3.2 details how we determine constraints on the observability of bright flares from TRAPPIST-1. In order to search for flares from TRAPPIST-1 with Evryscope, we sequence all Evryscope images of TRAPPIST-1's location and analyze them as described in the following sections.

Kepler observed the TRAPPIST-1 system in its short-cadence mode for one 80 day cycle, spanning 2016 December–2017 March; while these observations cover the same time range in which the Evryscope observed TRAPPIST-1, all K2 observations took place during the time of year when TRAPPIST-1 was not observable from CTIO. The FFD (the cumulative flare occurrence rate as a function of flare energy; see e.g., Gershberg 1972; Lacy et al. 1976, or Davenport et al. 2016 for details) of TRAPPIST-1 has been calculated from Kepler data by Vida et al. (2017) and Paudel et al. (2018). Both Vida et al. (2017) and Paudel et al. (2018) find the same flares in the K2 light curve of TRAPPIST-1, although their flare energy calculations differ, with energies calculated from raw data by Vida et al. (2017) being ∼10 times greater than those calculated later by Paudel et al. (2018) using data reduced from the K2 pipeline. We conduct our analysis with the more recent data of Paudel et al. (2018).

Using a custom python routine, we sequenced images of TRAPPIST-1 from the Evryscope for playback. By visual inspection of the image sequence, we could detect any excess emission indicative of flares at TRAPPIST-1's expected location in the image. We subtracted each image's median value from every pixel in the image to remove nightly variations in brightness due to changing sky background levels (caused by, for example, higher background from moonlight). We scaled the image contrast such that background noise—and thus excursions above it—was visible. Using the World Coordinate System solutions provided by the Evryscope pipeline (precise at the arcsecond, or 0.1 pixel, level), we marked the position of expected TRAPPIST-1 emission in each image. We then converted all images from FITS to PNG and sequenced them at a frame rate of 2 frames s⁻¹ using FFmpeg. An example set of consecutive frames from the image sequence is shown in Figure 1.

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We performed an initial visual search of the image sequence to identify image regions with significant deviations from noise. Since each image is centered on TRAPPIST-1's R.A. and decl. (after correcting for the star's proper motion), any emission from the star is expected to lie within a few pixels of the image center, in the region outlined in red in each image of Figure 1. Three flare candidates were visible in the image sequence; these candidates are shown in Figure 2. The detection levels of the three candidates are 3.0σ, 1.8σ, and 2.0σ, respectively, above the local noise floor. These candidates represent the most significant deviations from local noise found across the entire duration of the image sequence, but are not necessarily significant events as discussed below. Each candidate flare image was inspected by at least two people, and checked against the following criteria:

• 1.  
  Is the flare candidate more than one pixel in extent?
• 2.  
  Is the flare candidate's PSF shape consistent with nearby stars and signal level compared to the local image background?
• 3.  
  Is the flare candidate's brightness a 3σ variation from the noise?
• 4.  
  Is the detected peak position of the flare candidate close enough to the expected location of TRAPPIST-1 to be likely to have originated from the star?
• 5.  
  Is the flare candidate visible in at least two consecutive images?

We require the final criterion in order to ensure secure detections and to reduce false positives from fast transients, satellite trails, noise fluctuations, and other phenomena unrelated to TRAPPIST-1. In order to be detectable, the integrated flux of a flare must exceed the Evryscope's limiting magnitude for at least two minutes. Large flares detectable by the Evryscope likely persist for more than two minutes (Howard et al. 2019), and most have multiple peaks (Davenport et al. 2014), so a real flare would likely be visible in consecutive images.

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The first flare candidate, shown on the left in Figure 2, meets all criteria except the last—it is not visible in the frame immediately before its appearance, and there is no frame immediately following its appearance due to sunrise. The second candidate, at center in Figure 2, also does not appear in the frame before or after its appearance, nor does its detection level (1.8σ) meet the third criterion and so it is rejected. The third candidate, at right in Figure 2, does not appear in the previous frame and appears to move downward by 3 pixels in the next frame; however, its detection level (2.0σ) does not meet the third criterion, and its motion in the next frame is consistent with the local noise background, so it is likely caused by random noise fluctuations.

Assuming that a flare must be at least as bright as the Evryscope limiting magnitude (Ratzloff et al. 2019) in order to be visible, we estimate the expected number of false-positive flares using Gaussian statistics. Given the number of images observed, we would expect a 3σ deviation from the background far more often than the number of candidates actually observed. This suggests that our formal detection criterion is more stringent than 3σ, as expected given the extra filtering of candidates we applied. Detecting only three flare candidates is consistent with the false-positive estimate of 2.3 ± 1.5 flares one obtains assuming our detection limits are 4σ instead of 3σ. While we cannot exclude the possibility that each candidate was a real flare from the TRAPPIST-1 system, we cannot attach any significant probability of realness with only a single data point for all three candidates and a number of occurrences well within the expected number of false-positive signals. No flares from TRAPPIST-1 were confirmed in the Evryscope data set.

In order to determine the completeness limit of our method, we perform flare rejection and recovery simulations to find flare amplitudes and energies with 100% completeness. We can therefore establish a limit on how often flares of detectable energies can occur, given that we observed none. In order to do so, we run a series of Monte Carlo simulations to estimate the Evryscope minimum detectable flare energy for TRAPPIST-1.

Since TRAPPIST-1 is not visible to Evryscope when quiescent, we simulate its light curve as a one-day-long array of magnitude data matching the Evryscope's 2 minute cadence, with values equal to TRAPPIST-1's quiescent g' magnitude of 19.3. Following the methods described in Howard et al. (2018), we inject simulated flares into the light curve to determine the Evryscope's flare recovery rate for TRAPPIST-1. For 10,000 trials, flares are generated using the template described in Davenport et al. (2014) with possible peak contrasts (i.e., difference in magnitude between flare peak and quiescence) of 6.0, 5.5, 5.0, 4.75, 4.5, 4.25, 4.0, 3.75, 3.5, 3.25, and 3.0 in g'. An example simulated flare is shown in Figure 3.

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Flares are injected into the simulated light curve at randomly chosen epochs, and passed through checks to determine if at least two points of the flare are brighter than or equal to the Evryscope's limiting magnitude (to satisfy the final detection criterion given in Section 3.1). The limiting magnitude in each trial is drawn randomly from a distribution of Evryscope's measured limiting magnitude values at TRAPPIST-1's position between 2016 June and 2018 June, matching the time span covered by the Evryscope images analyzed in Section 3.1. The Evryscope limiting magnitudes are calculated from a comparison of the signal-to-noise ratio of detection of hundreds of nearby stars to catalog magnitudes from APASS (Henden et al. 2016); the full algorithm is described in Ratzloff et al. (2019). Figure 4 shows the distribution of measured limiting magnitudes. Simulated flares brighter than or equal to the Evryscope's limiting magnitude for two or more consecutive epochs are counted as successful recoveries; such flares would have been visible in images of TRAPPIST-1 had they occurred during Evryscope observations of the star. We define flare contrast, Δg', as the difference in g' magnitude between the flare peak and the star's quiescent g' magnitude.

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The total energy radiated by a flare depends on both its energy output at its peak and how long the flare lasts; flares with lower peak energies but long durations can have the same total energy output as flares with higher peak energies but much shorter durations. The equivalent duration (ED) is a measure of total flare energy output that takes account of this degeneracy between peak energy and duration, by calculating the normalized flux of the flare integrated over the length of the flare, yielding the ED of the flare in units of seconds. Here, the ED is calculated for each simulated flare as a first step toward calculating the flare energy. We calculate the ED following the method of Hawley et al. (2014). We use the trapezoidal rule to calculate ED as the "area under the curve" of each simulated flare, where the upper and lower limits of integration are the stop and start times of the flare, respectively. Using Figure 3 as an example, calculating the ED amounts to calculating the area enclosed by the quiescent emission (red points) as the x-axis and a curve tracing the flare emission (yellow points) as the enclosing function, from the flare start time to the flare end time. Figure 5 shows the ED distribution of simulated flares with sufficient contrast to be potentially visible in Evryscope data; the distribution's dropoff below Δg' ≈ 3.5 signifies that flares with contrasts less than Δg' ≲ 3.5 cannot boost TRAPPIST-1's quiescent magnitude of g' = 19.3 brighter than the Evryscope limiting magnitude of g' ≈ 16. Figure 6 shows the distribution of recovered flare time durations as a function of contrast, and Figure 7 shows the distribution of recovered flare EDs as a function of limiting magnitude.

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We estimate the Evryscope minimum recoverable flare energy using the ED and limiting magnitude distributions as follows.

• 1.  
  We take the median of the limiting magnitude distribution in Figure 4, finding that the Evryscope's median limiting magnitude, over all sky, moon, and cloud conditions at TRAPPIST-1's position is g' = 15.52.
• 2.  
  We check the simulated flare distribution against the median limiting magnitude obtained in step 1, to find the lowest flare contrast associated with that limiting magnitude. We take this contrast to be the average minimum recoverable flare contrast, since it occurs for the average value of limiting magnitude. The minimum flare contrast thus obtained is Δg' = 3.89.
• 3.  
  We recover the minimum ED from the distribution of flare EDs as a function of contrast (Figure 5, finding a minimum ED of 13,000 s for the minimum contrast of Δg' = 3.89 from step 2.
• 4.  
  Using TRAPPIST-1's quiescent g' magnitude (19.3) and its distance from Earth (12.1 pc), we calculate TRAPPIST-1's quiescent g' luminosity (10^27.4 erg s⁻¹) using the distance-magnitude relation. We then multiply the quiescent g' luminosity by the minimum recoverable ED to obtain the minimum recoverable g' flare energy, ${E}_{\min ,g^{\prime} }={10}^{31.5}$ erg.
• 5.  
  Finally, we convert the minimum recoverable flare energy from the Evryscope g' bandpass to bolometric energy using the energy partitions of Osten & Wolk (2015). To do so, we estimate the bolometric energy of a flare as being that of a 9000 K blackbody, finding that such a flare emits a fraction ${f}_{g^{\prime} }=0.19$ of its bolometric energy in the g' bandpass. Division of the minimum recoverable flare energy in g' by ${f}_{g^{\prime} }$ yields the minimum recoverable bolometric flare energy. We find the Evryscope minimum detectable bolometric flare energy is E_min = 10^32.2 erg. We note that the canonical 9000 K blackbody temperature provides a lower limit for flares' energies; a higher-temperature flare blackbody, as has been measured for some larger flares (e.g., Kowalski et al. 2010) would result in more energy radiated at short wavelengths.

We investigate the effects of TRAPPIST-1's flares on ozone depletion by applying the findings of Tilley et al. (2019) to the TRAPPIST-1 system. In that work, Tilley et al. (2019) estimate the flare rates and energies for a general M dwarf that would deplete ≥99.99% of the ozone column in a habitable-zone planet's atmosphere, given the probability of any given flare actually impacting a habitable-zone planet due to the geometry of the system. Tilley et al. (2019) simulate M-dwarf flares at a variety of energies and frequencies to study their effect on the ozone column of planets orbiting the M dwarf. They find that flares with energy E ≥ 10³⁴ erg are the primary contributor to ozone depletion; assuming the probability of any flare impacting the planet is 8.3%, they estimate that a flare rate of 0.4 such flares per day is sufficient to deplete ≥99.99% of the ozone column, or a worse case of 0.1 such flares per day if the probability of flare impact is 25% (Tilley et al. 2019).

Since our interest lies in determining whether the TRAPPIST-1 planets are in any danger of atmospheric ozone depletion from flares, we consider the case of 0.1 flares per day of ≥10³⁴ erg as a lowest effective energy for planetary ozone depletion, and calculate whether the FFD of TRAPPIST-1 is consistent with this case. In Figure 8, we plot the energy regime corresponding to ozone depletion in orange.

Tilley et al. (2019)'s model assumes a habitable-zone planet at a distance of 0.16 au from its host star, whereas the TRAPPIST-1 habitable-zone planets are approximately an order of magnitude closer than that to their star. A distance decrease of one order of magnitude corresponds to a flux increase of two orders of magnitude; however, UV flux accounts for ∼10% of combined ozone loss, with particle bombardment accounting for the remainder (Tilley et al. 2019). Shifting the ozone depletion region in Figure 8 as much as two orders of magnitude lower in energy still does not intersect the FFD. TRAPPIST-1 has at least an order of magnitude too low a flare rate to cause ≥99.99% atmospheric ozone loss for habitable-zone planets, even in the worst case scenario that assumes a 25% probability of any flare impacting a planet in the habitable zone. We conclude that TRAPPIST-1's current rate of flaring is unlikely to cause complete atmospheric ozone loss, if ozone is present in the atmospheres of its habitable-zone planets.

We investigate TRAPPIST-1's flares as catalysts for prebiotic chemistry, or abiogenesis, by applying the work of Rimmer et al. (2018) to the TRAPPIST-1 system. Rimmer et al. (2018) combine experimental lab chemistry with stellar physics to estimate how much energy due to flares would be necessary to power abiogenesis on Earthlike planets orbiting an M dwarf. Rimmer et al. (2018) determine reaction rates for hydroperoxide and cyanic acid, two reaction products necessary for the reaction pathway leading to synthesis of ribonucleic acid (RNA) pyrimidine nucleotides, the synthesis of which requires the input of 254 nm UV light in order to proceed.

Noting that a sustainable prebiotic chemistry for supporting life requires at least a 50% yield of each product in the nucleotide synthesis pathway, Rimmer et al. (2018) derive a formula for the minimum cumulative rate ν of flares at a given U-band energy E_u that provides the requisite yield. We use Rimmer et al. (2018)'s formula, expressed in cumulative flares per second for U-band flux,

$$\begin{eqnarray}&&\nu ({E}_{u})=8.0\times {10}^{27}\times {E}_{u}^{-1},\end{eqnarray} \tag{ 1 }$$

and convert to erg day⁻¹ in bolometric flux using blackbody conversion factors in Osten & Wolk (2015), obtaining an equation for the cumulative flare rate per day as a function of bolometric energy in erg,

$$\begin{eqnarray}&&\nu ({E}_{\mathrm{bol}})=6.6\times {10}^{33}\times {E}_{\mathrm{bol}}^{-1},\end{eqnarray} \tag{ 2 }$$

for which abiogenesis can proceed at rates sufficient for life. We then determine whether the FFD of TRAPPIST-1 overlaps with this energy regime; Figure 8 shows the FFD does not intersect the region that would meet Rimmer et al. (2018)'s criteria for supporting abiogenesis. While TRAPPIST-1's current flare rate is unlikely to deplete enough ozone from its planets to endanger any extant surface life, its current flare rate is also unlikely to provide enough UV flux to sustain prebiotic chemistry necessary for the synthesis of RNA nucleotides.

We estimate the cumulative annual UV flux from flares incident on each planet in the TRAPPIST-1 system, and compare to the quiescent UV flux Earth has experienced from our Sun. We do this in order to contextualize the flare UV flux, to analyze how it compares to the UV flux received by the only planet currently known to be inhabited. We focus on the UV-B (280–315 nm) region of the spectrum. Since UV-B light is energetic enough to damage biological tissues while being absorbed much less by Earthlike atmospheres than the higher-energy UV-C (Rugheimer et al. 2015), the UV-B flux reaching TRAPPIST-1's planets is particularly relevant for considerations of its surface habitability.

We sample the FFD in Figure 8 within the uncertainty range of the power-law fit, generating a distribution of the number of flares per day meeting or exceeding some minimum energy. We then generate a distribution of cumulative annual flare energies by the following process:

• 1.  
  Select one number of flares per day at random from the distribution of number of flares per day, convert from flares per day to flares per year, and round to the nearest integer. For example: 0.042 flares per day →15.33 flares per year ≈15 flares per year.
• 2.  
  Sample that number of flares from the FFD by generating flares of random energies, accepting those whose energies are consistent with values expected for their corresponding number of flares per day from the FFD, and rejecting those that are not consistent. We thereby obtain a distribution of possible energies for that number of flares per year. Example: sample 15 flares from the FFD, yielding a list of 15 bolometric flare energies consistent with the FFD.
• 3.  
  Sum up the flare energies from step 2, yielding a single cumulative flare energy per year—or cumulative annual flare energy.
• 4.  
  Repeat steps 1–3 for a total of 10,000 trials, yielding a distribution of cumulative annual bolometric flare energies.

We take the median of the distribution to be the estimated cumulative annual bolometric flare energy, and assign uncertainties by taking the 1σ confidence interval of the distribution.

To estimate the cumulative annual UV-B flare flux, we represent the spectral energy distribution of a flare as a 9000 K blackbody, which models the white-light continuum emission in flares while providing empirical fits for flare emission lines (Hawley et al. 2003; Kowalski et al. 2010). Modeling flares as blackbodies allows us to estimate their energy output in the UV-B region of the spectrum, using blackbody-dependent conversion relations for the fraction of bolometric energy encompassed by a given spectral band. Using this model, we convert the cumulative annual bolometric flare energies to cumulative annual UV-B flare energies.

From the cumulative annual UV-B flare energies, we estimate the cumulative annual UV-B flux received by each planet in the TRAPPIST-1 system, using their distances (Grimm et al. 2018) to calculate the flare UV-B flux incident at the top of each planet's atmosphere. In doing so, we assume all flares hit each planet, making our estimate an upper limit on the cumulative annual UV-B flux received by each planet due to flares from TRAPPIST-1. Lastly, to contextualize our results, we convert the cumulative annual top-of-atmosphere (TOA) UV-B flux at each planet to Earth-relative TOA UV-B flux, dividing each TRAPPIST-1 planet's TOA UV-B flux by the values of TOA UV-B flux for Earth given in Rugheimer et al. (2015). Using the tables provided by Rugheimer et al. (2015), we compare our estimates of flare TOA UV-B flux to the quiescent TOA UV-B flux received by Earth during three epochs: early Earth 3.9 billion years ago before the rise of life, the proterozoic era 2.0 billion years ago as oxygen levels rose in Earth's atmosphere, and modern Earth.

Figure 9 summarizes the estimated Earth-relative UV-B fluxes at each TRAPPIST-1 planet. As a whole, the TOA UV-B flare flux for all TRAPPIST-1 planets pales in comparison to that which Earth has experienced in any epoch. TRAPPIST-1b, the closest planet to the star, receives an order of magnitude less UV-B flux from flares than modern Earth receives from our Sun in quiescence; all other TRAPPIST-1 planets, being farther away from the star, decrease in flux received as they are successively farther away from the star. Earth receives more UV-B flux now than in the past (Rugheimer et al. 2015), so that each planet receives greater UV-B flux as a proportion of early Earth's UV-B flux than that of modern Earth. However, no planet receives UV-B flare flux anywhere close to that of early Earth. In particular, the habitable-zone planets c, d, and e (Gillon et al. 2017) currently receive more than an order of magnitude less quiescent and flare UV-B flux than Earth has ever received in its history. These results are consistent with our results in Sections 5.1 and 5.2, in which we determined that TRAPPIST-1's current bolometric flare energy output does not provide enough UV flux to completely deplete ozone in habitable-zone planet atmospheres, nor enough UV flux to catalyze the prebiotic reactions discussed in Rimmer et al. (2018).

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